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Field Guide to Quantum MechanicsFormat | Member Price | Non-Member Price |
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Pages: 146

ISBN: 9781510622821

Volume: FG44

*Glossary of Symbols**Glossary of Operators***Quantum Mechanics Formalism**- Quantum States, Kets, and State Space
- Elements of Dirac Notation
- Vector Spaces and Scalar Products
- Linear Operators and Commutators
- Hermitian Conjugation
- Bases
- Eigenvalue Equations
- Projectors
- Closure Relations
- Functions of Operators
**Postulates**- Postulates of Quantum Mechanics
- Eigenvalue and Collapse Postulates
- Probability Postulate
- Examples of Observables:
*Ĥ*,*&Xcirc;*, and*&Pcirc;*_{x} **Bases and Representations**- Calculating Quantities in Quantum Mechanics
- Calculating Quantities Using a Discrete Basis
- Discrete Representations
- Transformation of Discrete Representation
- Continuous Representations:
*&Xcirc;*,*&Pcirc;*_{x} - Continuous Representations: Wavefunctions
- Calculating Quantities Using a Continuous Basis
- Operators in the
*&Xcirc;*Representation *&Xcirc;*and*&Pcirc;*Representations: Eigenkets and Operators_{x}*&Xcirc;*and*&Pcirc;*Representations: Fourier Transforms_{x}- Tensor Products: Merging State Spaces
**Operators**- Operator Definitions and Operator Manipulation
- Expectation Values
- Commutation Relations
- Non-Commuting Operators, Uncertainty Relations
- Complete Sets of Commuting Observables
- CSCOs for Specific Problems
**Wavefunctions**- Properties of Wavefunctions
- Wave-Like Properties of Matter
- Graphical Interpretation of the Schrodinger Equation
- Graphical Interpretation: Example
- Superpositions, Relative and Global Phases
- Probability Currents
**Time Dependence, Transformations, "Pictures"**- Unitary Transformations
- Common Unitary Operators
- Conservative Systems
- Stationary States
- Time-Dependent Reference Frames
- Schrodinger, Heisenberg, and Interaction Pictures
- Schrodinger Picture: Expectation Value Dynamics
- Heisenberg Picture: Operators and Dynamics
- Interaction Picture
**Exactly Solvable Problems**- Exactly Solvable Problems in One Dimension
- Free Particle and Delta Function Potential Well
- Infinite Square Well
- Potential Barrier: Transmission and Reflection
- Potential Barrier: Energy above Barrier
- Potential Barrier: Tunneling
- Potential Barrier: Examples
- 1D Quantum Harmonic Oscillator
- Harmonic Oscillator: Energy Eigenfunctions
- Harmonic Oscillator: Ladder Operators
- Harmonic Oscillator: Properties and Dynamics
- Harmonic Oscillator: Fourier Transforms
- Coherent States (Quasi-Classical States)
- Phase-Space Diagrams
- Phase-Space Diagrams: Examples
- 3D Quantum Harmonic Oscillator
**Angular Momentum**- Angular Momentum: Definitions
- Angular Momentum: Eigenvalues and Eigenstates
- Orbital Angular Momentum: Operators
- Orbital Angular Momentum: Position Representation
- Spin Angular Momentum
- Spin Angular Momentum:
*s*= 1/2 - Pauli Spin Operators
- Angular Momentum
*j*= 1 - Magnetic Dipole Moments and Magnetic Fields
- Gyromagnetic Ratios and
*g*-Factors - Magnetic Moment Dynamics: Uniform Fields
- Magnetic Moment Dynamics: Gradient Fields
**Two-Level Systems and Spin 1/2**- Two-Level Systems
- Rabi Oscillations
- The Bloch Vector
- The Bloch Sphere
- Spin 1/2 in a Uniform Magnetic Field
- Spin 1/2 in a Uniform Magnetic Field: Dynamics
- Bloch Vector Dynamics: Examples
**Addition of Angular Momentum**- Addition of Two Angular Momenta
- Total Angular Momentum Basis
- Addition of Angular Momentum: Example
- Addition of Angular Momentum: Comments
- Clebsch-Gordan Coefficients
- Clebsch-Gordan Coefficients: Usage
- Clebsch-Gordan Coefficients: Examples
**Approximation Methods**- Ritz Variational Method
- Stationary Perturbation Theory
- Degenerate Stationary Perturbation Theory
- Time-Dependent Perturbation Theory
- TDPT: First-Order Solution
- Fourier Transform Pairs for Pulse Perturbations
- TDPT: Harmonic Perturbations
**Hydrogen and Atomic Structure**- Central Potential Problems
- "Spinless" Hydrogen: Energy Eigenvalues
- Spinless Hydrogen: Energy Eigenfunctions
- Hydrogen Radial Wavefunctions
- Spherical Harmonics
- Atomic Angular Momentum Quantum Numbers
- Fine Structure of Hydrogen: Perturbation Terms
- Fine Structure of Hydrogen: Solutions
- Hyperfine Structure of Hydrogen
- Zeeman Effect in Hydrogen:
*n*= 1 - Zeeman Effect in Hydrogen:
*n*= 1 Solutions - Spectroscopic Notation and Term Symbols
**Identical Particles**- Identical Particles: Two Particles
- Identical Particles: Three or More Particles
- Identical Particles: Occupation Number Basis
- Identical Particles: Occupation Number Basis States
**Appendix: Mathematics Reference, Tables, and Constants**- Miscellaneous Symbols and Notation
- Linear Algebra Basics
- Eigenvalue Equations in Linear Algebra
- Spherical Coordinates
- Operators in Spherical Coordinates
- Properties of 1D Gaussian Wavefunctions
- Clebsch-Gordan Coefficient Tables:
*J*_{1}× 1/2 - Clebsch-Gordan Coefficient Tables:
*J*_{1}× 1 - Clebsch-Gordan Coefficient Tables:
*J*_{1}× 3/2 - Clebsch-Gordan Coefficient Tables: 2 × 2
- Integrals of Exponential Forms
- Identities and Series Expansions
- Dimensional Units (SI)
- Common Physical Constants (to Four Significant Digits)

This *Field Guide* is a condensed reference to the concepts,
definitions, formalism, equations, and problems of quantum
mechanics. Many topics covered in quantum mechanics courses
are included, while numerous details and derivations are
necessarily omitted. This *Field Guide* is envisioned to appeal to
undergraduate and graduate students engaged in quantum
mechanics research or courses; to professors, as an aid in teaching
and research; and to professional physicists and engineers
pursuing cutting-edge applications of quantum mechanics. The
mathematical formalism used here involves Dirac notation, with
which the reader should be (or become) familiar to make the most
of this *Field Guide*. Nevertheless, readers who are not yet familiar
with this formalism should be able to utilize various aspects of
this *Field Guide*, especially with extra attention directed to the
basic concepts addressed in the first few sections.

I owe sincere thanks to mentors, professors, colleagues, collaborators, and friends too numerous to single out by name who have taught, motivated, and encouraged me throughout more than three decades of studying quantum physics. Since joining the University of Arizona faculty, the unwavering support and partnership of local and international colleagues and collaborators has been indispensable in learning and appreciating many of the numerous facets of this fascinating subject.

I am especially grateful to two physicists in particular who set in motion the trajectory of my eventual career while I was still in high school: the late Jeff Chalk, who first introduced me to Schrodinger's equation and quantum mechanics; and Al Rosenberger, my first laboratory mentor, who launched my interest in lasers, optics, and experimental physics.

This *Field Guide* is dedicated to Jeff and Al, and to the students
who have worked in my labs, sat through my courses, and made
my career as a mentor and educator profoundly fulfilling.

**Brian P. Anderson**

June 2019

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