Elements of Quantum Mechanics provides a solid grounding in the fundamentals of quantum theory and is designed for a first semester graduate or advanced undergraduate course in quantum mechanics for chemistry, chemical engineering, materials science, and physics students. The text includes full development of quantum theory. It begins with the most basic concepts of quantum theory, assuming only that students have some familiarity with such ideas as the uncertainty principle and quantized energy levels. Fayer's accessible approach presents balanced coverage of various quantum theory formalisms, such as the Schr:odinger representation, raising and lowering operator techniques, the matrix representation, and density matrix methods. He includes a more extensive consideration of time dependent problems than is usually found in an introductory graduate course. Throughout the book, sufficient mathematical detail and classical mechanics background are provided to enable students to follow the quantum mechanical developments and analysis of physical phenomena. Fayer provides many examples and problems with fully detailed analytical solutions. Creating a distinctive flavor throughout, Fayer has produced a challenging text with exercises designed to help students become fluent in the concepts and language of modern quantum theory, facilitating their future understanding of more specialized topics. The book concludes with a section containing problems for each chapter that amplify and expand the topics covered in the book. A complete and detailed solution manual is available.
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About the Author
Michael D. Fayer, the D. M. Ehrsam and E. C. Franklin Professor of Chemistry at Stanford University, is a member of the National Academy of Sciences, and has received the American Chemical Society E. Bright Wilson Award for Spectroscopy, the American Physical Society Earl K. Plyler Prize for Molecular Spectroscopy, and the Optical Society of America Ellis R. Lippincott Award. He has taught graduate quantum mechanics at Stanford for over thirty years.
A complete set of Power Point lectures for teaching using his book is available on his web site (http://www.stanford.edu/group/fayer/), and he will provide the complete Problem and Solution Manual in Word format to instructors upon request.
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Profile of Michael D. Fayer
By Melissa Marino
Introduction
In the air we breathe, the water we drink, and the glasses we may need to read these words, molecules are on the move. Even the hardest of materials abounds with shaking, vibrating, bouncing, and twisting at the molecular level. These motions, which are invisible to the unaided eye, give our world form and function, imparting the physical properties we detect with our everyday senses.
Using sophisticated ultrafast spectroscopic methods, Michael D. Fayer, the David Mulvane Ehrsam and Edward Curtis Franklin Professor of Chemistry at Stanford University, has been working out these invisible movements for more than a third of a century
Electric youth
A career in science seems somewhat inevitable growing up in a family like Fayer's. His father William, an electrical engineer at the dawn of the modern electronics era, exuded excitement for science and technology and easily imparted that fascination to his son.
"When I was very young, maybe 6 or 7, my father came home one day, and he held up this little thing in his hand and said, 'This is a transistor. Soon there will be no more vacuum tubes!' This is how I grew up."
His father was correct. Soon vacuum tubes, the hot, bulky components that powered early electronics, were obsolete, replaced with the tiny transistor that led the way to the downsized electronics of today. Always at the forefront of technology, William Fayer not only made science and electronics his career, but his hobby. With an electronics laboratory in the basement, there were always electronic "toys" - oscilloscopes, signal generators, and soldering irons - with which a young boy could experiment.
Later, electronics gave way to pyrotechnics and photography - hobbies that introduced Fayer to the fascinating world of chemistry.
"With chemistry, you can make all sorts of nifty things, like fireworks," says Fayer. And the "complicated chemical process" of photography became one of Fayer's extracurricular passions.
Science was ingrained in him, and Fayer anticipated a career in science from a very young age.
"It sounds crazy, but when I was very young, 8 or 10 years old, I thought I was going to grow up and become a physics professor."
This youthful certainty quickly changed though upon entering college at the University of California at Berkeley. Although his plan was to major in physics, a summer research program led him to work with a chemist.
"It turned out that the types of initial equipment that needed to built used radiofrequency electronics," Fayer says. Through his father, the electronics instrumentation in the house and the lab, and his experience as an amateur radio operator in junior high school and high school, Fayer knew how to build electronic equipment. "So, as a sophomore, I helped build up a new lab."
Fayer continued research throughout his undergraduate years and later as a graduate student studying physical chemistry.
"Physical chemistry is the physics of molecules. When you look at the world around you, everything is controlled by processes that happen at a 1 nanometer length scale - the size of molecules. The chemical reactions and processes that cause disease and make life, all of this is chemistry. The things that affect you in your day to day life are all chemistry."
Seeing the light
After finishing his doctorate at Berkeley in 1974, Fayer was offered a faculty position at Stanford University at the age of 26 - even then, a rare event without the now requisite "postdoc." At Stanford, he began the eclectic mix of experiments that has run the gamut from water, flames, and diamonds to proteins and artificial cell membranes.
"My interests are in trying to understand at a molecular level how complicated systems of molecules evolve in time and how intermolecular interactions - how molecules 'feel' each other and move relative to each other - give systems their properties."
To study these nanoscopic processes takes some sophisticated instrumentation. As a graduate student, Fayer had been working with magnetic resonance, which used pulses of microwave energy to detect and measure the dynamics of "spins" of electrons in a material. These types of techniques form the basis of modern magnetic resonance imaging (MRI).
In the early 1970s, Fayer had read a papers by about a technique called the Photon Echo that used optical - visible and ultraviolet (UV) light - pulses instead of the radio frequency pulses employed in magnetic resonance. This sparked Fayer's interest and, as an independent investigator, he began branching out and experimenting with these new techniques.
Although inspired by the early photon echo experiments, he found that this potentially useful technique wasn't amenable to measuring the ultrafast dynamics of molecules that interested him. So Fayer expanded the techniques using tunable picosecond lasers (ultrafast at the time) to be able to use the right color of light for the molecules of interest and to make the measurements fast enough to study molecular dynamics in condensed matter materials. He also began apply other nonlinear optical pulse sequences to the study of dynamics of molecular processes.
One of the methods that Fayer's group began developing for application to a wide variety of chemical and materials problems is the transient grating technique, now one of the most widely used nonlinear optical techniques in chemistry. In a transient grating experiment, two ultrafast pulses of light make a hologram in the sample. A delayed third light pulse is used to read out the time evolution of the hologram. Transient grating experiments were used to measure diverse phenomena, such as the mechanical properties of membranes, heat transport in materials, electronic excited state dynamics, the rotation of molecules in liquids and liquid crystals, and the velocity of atoms in flames. The technique is "nonlinear" because one shoots three pulses of laser light into a sample at different times, and the sample generates a fourth pulse of light, the signal, which carries the information about molecular processes and properties.
Fayer used transient gratings and a variety of other methods and theory to study electronic excitation transport - a process where light energy absorbed by one molecules jumps to another. The most famous example of this is the excitation transfer that happens between chlorophyll molecules in the initial stage of photosynthesis. For example, Fayer's group used excitation transfer in polymers to study their structure.
One of the projects he is most proud of was the group's work on low temperature glasses. "Glasses show up all over the place," Fayer explains. Unlike crystalline solids, glasses - like window glass, plastics, and other organic solids - have no regular pattern in the way the molecules arrange themselves. "They're like a liquid that is solid. And even if you go to very low temperatures (a few degrees Kelvin), the molecules can still rearrange themselves."
"There was a tremendous interest in understanding the dynamics of glasses because they're disordered." Previous research using a slow optical technique called "hole burning" missed the essence of the problem, that is, that glass dynamics occur on all time scales, from extremely fast (picoseconds) to very slow (thousands of seconds and longer). Using a variety of optical techniques photon echoes, stimulated photon echoes, fast to slow time dependent hole burning experiments Fayer's group was able to detail the molecular dynamics of glasses over a wide range of timescales, from picoseconds to 10,000 seconds.
They proved theoretically that all of these experiments and a variety of other optical techniques are equivalent, but operate on different time scales, "We showed the relationship between these slow, fast and medium time scale experiments. There wasn't one single experiment that was going to provide all of the important information."
Infrared shift
Although he had much success with these ultrafast nonlinear optical experiments, visible and UV light were not ideal for some of the other problems Fayer wanted to address.
"In the 1990s, we started thinking about...using infrared (IR) pulses to do similar nonlinear experiments on the vibrations of molecules," Fayer recalls.
When an infrared pulse hits a molecule, the bonds between the atoms vibrate, and Fayer's next step was to measure these "vibrational echoes," similar to spin echoes measured by NMR and photon echoes measured by optical techniques. But again, the available techniques had to be tweaked.
Fayer notes his good fortune in being at Stanford, whose physics department had invented the Free Electron Laser (FEL), a giant linear accelerator the size of two football fields the provided input for a type of laser that could produce short light pulses. The physicists were trying to develop a FEL to work in the infrared - a project in line with Fayer's interests.
"I became the developer with them of applying FELs to look at molecular systems with ultrafast IR pulses," Fayer says. In 1993, Fayer's group performed the first "vibrational echo" experiments on molecules in liquid and glass.
Following these early one dimensional experiments, the Fayer group now uses two dimensional infrared (2D-IR) vibrational echo spectroscopy, akin to 2D NMR, to captured under thermal equilibrium conditions the exceptionally rapid formation and dissolution of solute-solvent complexes and molecular isomerization - reactions too fast to be measured by other methods.
One of Fayer's key targets with the infrared techniques has been water. A deceptively simple molecule, water is nature's most important solvent.
"Water as a solvent makes a tremendous number of chemical processes possible. It enables charges to move, electron transfer, proton transfer...its ability to facilitate chemical and biological processes depends on water's ability to rearrange its structure," says Fayer. Fayer's group used 2D-IR vibrational echo spectroscopy to obtained a detailed picture of the very fast (femtosecond to picosecond) motions of water molecules in bulk water.
In nature and in technological applications like fuel cells, water is often confined to very small, tight niches. Fayer's group has done experiments on as few as 40 water molecules and has found that the properties of such nanoconfined water are wildly different from those of bulk water in the ocean or in a drinking glass.
Fayer used infrared spectroscopy to study water in reverse micelles - tiny artificial "bubbles" that can encase miniscule amounts of water. In these tiny pools of water, containing only a few hundred molecules of water, "the motions of the water molecules are very different from bulk water," notes Fayer.
One application in which confined water plays an important role is in modern fuel cells. Recently, Fayer made the first measurements of the behavior of water inside a fuel cell membrane. Understanding such dynamics could be crucial to developing hydrogen fuel cells as an alternative fuel source to power our automobiles.
Fayer probed another interesting aspect of water's behavior - how it behaves in a highly concentrated salt solution.
"There had been claims that in these highly concentrated salt solutions, the ability of water molecules to change their orientation, to restructure, slowed down by a factor of 30 to 50," Fayer says. But using 2D-IR vibrational echo experiments, Fayer has found that even in an extremely concentrated salt solutions, the slowing of the dynamics was about a factor of 3.
"It really shows that water, even in the presence of charges, can still restructure, can change its geometry really rapidly, which is really important for processes like proton transfer and protein folding"
Fayer is continuing to probe the mysteries of nature's favorite solvent, with his most recent experiments comparing the effects and interactions of confinement and charged interfaces.
With no shortage of molecules to study and experiments to run, Fayer still conveys the youthful enthusiasm for science that he acquired from his father and his early mentors. Now in his 38th year at Stanford, retirement, he says, is not an option.
"I've been here over a third of a century - and you know you're getting old when you measure things in fractions of centuries," he quips. "I hope to hold some record for being at Stanford longer than anybody."
Echoes of the young tinkerer continue to resound - in his work and in his hobbies. Fayer has kept up with his lifelong passion for photography - which, although once a chemistry experiment itself, has now evolved into the digital age. In place of chemical baths and film, Fayer's photography tools now include a digital camera and photo-editing software.
Like photography, science continues to change, with Fayer adjusting course along with it. He wouldn't have it any other way.
"Science is never boring. It can be frustrating and difficult and trying, but it's never boring. I don't know how to be bored."
By Melissa Marino
Introduction
In the air we breathe, the water we drink, and the glasses we may need to read these words, molecules are on the move. Even the hardest of materials abounds with shaking, vibrating, bouncing, and twisting at the molecular level. These motions, which are invisible to the unaided eye, give our world form and function, imparting the physical properties we detect with our everyday senses.
Using sophisticated ultrafast spectroscopic methods, Michael D. Fayer, the David Mulvane Ehrsam and Edward Curtis Franklin Professor of Chemistry at Stanford University, has been working out these invisible movements for more than a third of a century
Electric youth
A career in science seems somewhat inevitable growing up in a family like Fayer's. His father William, an electrical engineer at the dawn of the modern electronics era, exuded excitement for science and technology and easily imparted that fascination to his son.
"When I was very young, maybe 6 or 7, my father came home one day, and he held up this little thing in his hand and said, 'This is a transistor. Soon there will be no more vacuum tubes!' This is how I grew up."
His father was correct. Soon vacuum tubes, the hot, bulky components that powered early electronics, were obsolete, replaced with the tiny transistor that led the way to the downsized electronics of today. Always at the forefront of technology, William Fayer not only made science and electronics his career, but his hobby. With an electronics laboratory in the basement, there were always electronic "toys" - oscilloscopes, signal generators, and soldering irons - with which a young boy could experiment.
Later, electronics gave way to pyrotechnics and photography - hobbies that introduced Fayer to the fascinating world of chemistry.
"With chemistry, you can make all sorts of nifty things, like fireworks," says Fayer. And the "complicated chemical process" of photography became one of Fayer's extracurricular passions.
Science was ingrained in him, and Fayer anticipated a career in science from a very young age.
"It sounds crazy, but when I was very young, 8 or 10 years old, I thought I was going to grow up and become a physics professor."
This youthful certainty quickly changed though upon entering college at the University of California at Berkeley. Although his plan was to major in physics, a summer research program led him to work with a chemist.
"It turned out that the types of initial equipment that needed to built used radiofrequency electronics," Fayer says. Through his father, the electronics instrumentation in the house and the lab, and his experience as an amateur radio operator in junior high school and high school, Fayer knew how to build electronic equipment. "So, as a sophomore, I helped build up a new lab."
Fayer continued research throughout his undergraduate years and later as a graduate student studying physical chemistry.
"Physical chemistry is the physics of molecules. When you look at the world around you, everything is controlled by processes that happen at a 1 nanometer length scale - the size of molecules. The chemical reactions and processes that cause disease and make life, all of this is chemistry. The things that affect you in your day to day life are all chemistry."
Seeing the light
After finishing his doctorate at Berkeley in 1974, Fayer was offered a faculty position at Stanford University at the age of 26 - even then, a rare event without the now requisite "postdoc." At Stanford, he began the eclectic mix of experiments that has run the gamut from water, flames, and diamonds to proteins and artificial cell membranes.
"My interests are in trying to understand at a molecular level how complicated systems of molecules evolve in time and how intermolecular interactions - how molecules 'feel' each other and move relative to each other - give systems their properties."
To study these nanoscopic processes takes some sophisticated instrumentation. As a graduate student, Fayer had been working with magnetic resonance, which used pulses of microwave energy to detect and measure the dynamics of "spins" of electrons in a material. These types of techniques form the basis of modern magnetic resonance imaging (MRI).
In the early 1970s, Fayer had read a papers by about a technique called the Photon Echo that used optical - visible and ultraviolet (UV) light - pulses instead of the radio frequency pulses employed in magnetic resonance. This sparked Fayer's interest and, as an independent investigator, he began branching out and experimenting with these new techniques.
Although inspired by the early photon echo experiments, he found that this potentially useful technique wasn't amenable to measuring the ultrafast dynamics of molecules that interested him. So Fayer expanded the techniques using tunable picosecond lasers (ultrafast at the time) to be able to use the right color of light for the molecules of interest and to make the measurements fast enough to study molecular dynamics in condensed matter materials. He also began apply other nonlinear optical pulse sequences to the study of dynamics of molecular processes.
One of the methods that Fayer's group began developing for application to a wide variety of chemical and materials problems is the transient grating technique, now one of the most widely used nonlinear optical techniques in chemistry. In a transient grating experiment, two ultrafast pulses of light make a hologram in the sample. A delayed third light pulse is used to read out the time evolution of the hologram. Transient grating experiments were used to measure diverse phenomena, such as the mechanical properties of membranes, heat transport in materials, electronic excited state dynamics, the rotation of molecules in liquids and liquid crystals, and the velocity of atoms in flames. The technique is "nonlinear" because one shoots three pulses of laser light into a sample at different times, and the sample generates a fourth pulse of light, the signal, which carries the information about molecular processes and properties.
Fayer used transient gratings and a variety of other methods and theory to study electronic excitation transport - a process where light energy absorbed by one molecules jumps to another. The most famous example of this is the excitation transfer that happens between chlorophyll molecules in the initial stage of photosynthesis. For example, Fayer's group used excitation transfer in polymers to study their structure.
One of the projects he is most proud of was the group's work on low temperature glasses. "Glasses show up all over the place," Fayer explains. Unlike crystalline solids, glasses - like window glass, plastics, and other organic solids - have no regular pattern in the way the molecules arrange themselves. "They're like a liquid that is solid. And even if you go to very low temperatures (a few degrees Kelvin), the molecules can still rearrange themselves."
"There was a tremendous interest in understanding the dynamics of glasses because they're disordered." Previous research using a slow optical technique called "hole burning" missed the essence of the problem, that is, that glass dynamics occur on all time scales, from extremely fast (picoseconds) to very slow (thousands of seconds and longer). Using a variety of optical techniques photon echoes, stimulated photon echoes, fast to slow time dependent hole burning experiments Fayer's group was able to detail the molecular dynamics of glasses over a wide range of timescales, from picoseconds to 10,000 seconds.
They proved theoretically that all of these experiments and a variety of other optical techniques are equivalent, but operate on different time scales, "We showed the relationship between these slow, fast and medium time scale experiments. There wasn't one single experiment that was going to provide all of the important information."
Infrared shift
Although he had much success with these ultrafast nonlinear optical experiments, visible and UV light were not ideal for some of the other problems Fayer wanted to address.
"In the 1990s, we started thinking about...using infrared (IR) pulses to do similar nonlinear experiments on the vibrations of molecules," Fayer recalls.
When an infrared pulse hits a molecule, the bonds between the atoms vibrate, and Fayer's next step was to measure these "vibrational echoes," similar to spin echoes measured by NMR and photon echoes measured by optical techniques. But again, the available techniques had to be tweaked.
Fayer notes his good fortune in being at Stanford, whose physics department had invented the Free Electron Laser (FEL), a giant linear accelerator the size of two football fields the provided input for a type of laser that could produce short light pulses. The physicists were trying to develop a FEL to work in the infrared - a project in line with Fayer's interests.
"I became the developer with them of applying FELs to look at molecular systems with ultrafast IR pulses," Fayer says. In 1993, Fayer's group performed the first "vibrational echo" experiments on molecules in liquid and glass.
Following these early one dimensional experiments, the Fayer group now uses two dimensional infrared (2D-IR) vibrational echo spectroscopy, akin to 2D NMR, to captured under thermal equilibrium conditions the exceptionally rapid formation and dissolution of solute-solvent complexes and molecular isomerization - reactions too fast to be measured by other methods.
One of Fayer's key targets with the infrared techniques has been water. A deceptively simple molecule, water is nature's most important solvent.
"Water as a solvent makes a tremendous number of chemical processes possible. It enables charges to move, electron transfer, proton transfer...its ability to facilitate chemical and biological processes depends on water's ability to rearrange its structure," says Fayer. Fayer's group used 2D-IR vibrational echo spectroscopy to obtained a detailed picture of the very fast (femtosecond to picosecond) motions of water molecules in bulk water.
In nature and in technological applications like fuel cells, water is often confined to very small, tight niches. Fayer's group has done experiments on as few as 40 water molecules and has found that the properties of such nanoconfined water are wildly different from those of bulk water in the ocean or in a drinking glass.
Fayer used infrared spectroscopy to study water in reverse micelles - tiny artificial "bubbles" that can encase miniscule amounts of water. In these tiny pools of water, containing only a few hundred molecules of water, "the motions of the water molecules are very different from bulk water," notes Fayer.
One application in which confined water plays an important role is in modern fuel cells. Recently, Fayer made the first measurements of the behavior of water inside a fuel cell membrane. Understanding such dynamics could be crucial to developing hydrogen fuel cells as an alternative fuel source to power our automobiles.
Fayer probed another interesting aspect of water's behavior - how it behaves in a highly concentrated salt solution.
"There had been claims that in these highly concentrated salt solutions, the ability of water molecules to change their orientation, to restructure, slowed down by a factor of 30 to 50," Fayer says. But using 2D-IR vibrational echo experiments, Fayer has found that even in an extremely concentrated salt solutions, the slowing of the dynamics was about a factor of 3.
"It really shows that water, even in the presence of charges, can still restructure, can change its geometry really rapidly, which is really important for processes like proton transfer and protein folding"
Fayer is continuing to probe the mysteries of nature's favorite solvent, with his most recent experiments comparing the effects and interactions of confinement and charged interfaces.
With no shortage of molecules to study and experiments to run, Fayer still conveys the youthful enthusiasm for science that he acquired from his father and his early mentors. Now in his 38th year at Stanford, retirement, he says, is not an option.
"I've been here over a third of a century - and you know you're getting old when you measure things in fractions of centuries," he quips. "I hope to hold some record for being at Stanford longer than anybody."
Echoes of the young tinkerer continue to resound - in his work and in his hobbies. Fayer has kept up with his lifelong passion for photography - which, although once a chemistry experiment itself, has now evolved into the digital age. In place of chemical baths and film, Fayer's photography tools now include a digital camera and photo-editing software.
Like photography, science continues to change, with Fayer adjusting course along with it. He wouldn't have it any other way.
"Science is never boring. It can be frustrating and difficult and trying, but it's never boring. I don't know how to be bored."
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Most Helpful Customer Reviews
11 of 11 people found the following review helpful:
4.0 out of 5 stars
Very good, but short,
By Jeff (Chicago, IL United States) - See all my reviews
This review is from: Elements of Quantum Mechanics (Hardcover)
This book has an excellent treatment of quantum mechanics, especially density matrices. This book lacks both the confusion and perhaps depth of a bigger book. It is definately for chemists, and ideal for spectroscopists like Fayer. Physicists will definately find better books by physicists.I don't know if it's worth 72 for the amount covered. Fayer also made up his own notation for operators, which gets a little obnoxious.
11 of 12 people found the following review helpful:
5.0 out of 5 stars
Fresh approach to teaching quantum mechanics,
By A Customer
This review is from: Elements of Quantum Mechanics (Hardcover)
This excellent graduate level textbook offers an overview ofthe basic concepts of quantum mechanics with just the right amount of material and mix of fundamental theory and practical applications.It contains a more comprehensive introduction compared with other books that focus solely on the Schroedinger picture. Operator techniques and the Dirac notation are introduced in a clear way which should be widely accessible to Chemistry Graduate students.Its time dependent viewpoint is very intuitive. It covers material, such as an introduction to density matrices, that is essential for reading the modern literature.The book further includes topics such as excitons and wavepackets which are not usually covered in graduate classes. Instructors can get an entire power point set of lectures for the course from the author which makes it a pleasure to teach from this book. I highly recommend this text.
7 of 7 people found the following review helpful:
5.0 out of 5 stars
Excellent for a Course or Self-study!,
Amazon Verified Purchase(What's this?)
This review is from: Elements of Quantum Mechanics (Hardcover)
I am a retired engineering manager who favors studying theoretical physics over golf. I recently completed a self-directed study of quantum mechanics using several books along with a variety of lectures and materials available on the web. I found when the going got rough with difficult material, I kept returning to Fayer's concise, accurate explanations, which cleared things up. Although this book is designed for a graduate course in chemistry or other fields, it excellent for self-study, particularly in conjunction with the lecture slides available on Fayer's web site. Highly recommended!
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Inside This Book
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First Sentence:
By the late 1920s, several formulations of quantum theory had been put forward. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
transition dipole bracket, first metal atom, harmonic oscillator wave packet, dipole brackets, energy eigenvalue problem, new eigenket, momentum eigenkets, antisymmetric spatial function, momentum eigenvalue problem, acceptable wavefunction, arbitrary ket, other kets, electronic excitation transfer, bra corresponding, perturbation theory treatment, closed bracket, electron labels, absolute value squared, plane rotor, infinite box, momentum eigenfunctions, hydrogen molecule ion, quantum harmonic oscillator, ket vector, nondegenerate states Key Phrases - Capitalized Phrases (CAPs): (learn more)
Pauli Principle, Pauli Exclusion Principle, Change of Basis Set New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
By the late 1920s, several formulations of quantum theory had been put forward. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
transition dipole bracket, first metal atom, harmonic oscillator wave packet, dipole brackets, energy eigenvalue problem, new eigenket, momentum eigenkets, antisymmetric spatial function, momentum eigenvalue problem, acceptable wavefunction, arbitrary ket, other kets, electronic excitation transfer, bra corresponding, perturbation theory treatment, closed bracket, electron labels, absolute value squared, plane rotor, infinite box, momentum eigenfunctions, hydrogen molecule ion, quantum harmonic oscillator, ket vector, nondegenerate states Key Phrases - Capitalized Phrases (CAPs): (learn more)
Pauli Principle, Pauli Exclusion Principle, Change of Basis Set New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
3
books
cite this book:
- Physical Chemistry by Robert J. Silbey on page 343, and page 392
- The Chemical Bond: A Fundamental Quantum-Mechanical Picture (Springer Series in Chemical Physics) by Tadamasa Shida in Back Matter
- The Spectra and Dynamics of Diatomic Molecules: Revised and Enlarged Edition by Helene Lefebvre-Brion in Back Matter
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