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Preface
The Fundamental Concepts of Quantum Mechanics
The Need to Abandon Classical Physics
Quantum Solution—The First Five Postulates
Expectation Value, Variance, and General Considerations
Observables with Continuum Spectrum and Wavefunction
Langrangian and Hamiltonian Formalism
Lagrangian Formalism—Euler-Lagrange Equations
Classical Particle in an Electromagnetic Field
Hamiltonian Formalism—Legendre Transform—Hamilton's Equations
Symmetries and Conservation Laws—Poisson Bracket
The Sixth Postulate
Generalization of the Fifth Postulate: Schrödinger Equation
Heisenberg's Uncertainty Principle
Summary of What We Have Learned So Far
Exercises
Quantum Systems in Finite-Dimensional Hilbert Spaces
From Operators to Matrices, from Kets to Column Vectors …
Quantum Systems with Two States—Pauli Matrices
Exercises
Quantum Particle in One Dimension
Momentum Operator and Hamiltonian
Continuity Equation
Piecewise Constant Potential
Piecewise Constant Potential with Dirac Deltas
Reflection and Transmission Coefficients
Harmonic Potential
Raising and Lowering Operators
Eigenfunctions and Hermite Polynomials
Coherent States
Exercises
Quantum Particle in Three Dimensions
Momentum Operator and Hamiltonian
Virial Theorem
Separable Hamiltonians
Quantum Particle in an Electromagnetic Field
Continuity Equation
Static Electromagnetic Field
Angular Momentum
Simultaneous Eigenkets of ModifyingAbove upper L With caret squared2 and ModifyingAbove upper L With caret Subscript zz
Angular Momentum in Polar Coordinates
Spherical Harmonics
Laplacian in Polar Coordinates
Central Potential
Hydrogen Atom
Semiclassical Derivation of Hydrogenoid Levels
Radial Functions
Exercises
Spin and Addition of Angular Momenta
Spin
Matrix Representation of Spin Operators
Spin 1 divided by 21/2 and Spin 11
Spin-Orbit Interaction
Addition of Angular Momenta
Hydrogen Atom with Spin-Orbit Interaction
Heisenberg Hamiltonian for Magnetic Systems
Exercises
Approximation Methods
Perturbation Theory: Correction to Energy Levels
Correction to Nondegenerate Levels
Correction to Degenerate Levels
Perturbation Theory: Time Evolution
Fermi Golden Rule
Radiation-Matter Interaction
Variational Method
Exercises
Appendix A Dirac Delta: Definition and Properties
Appendix B Levi-Civita Tensor: Definition and Properties
Appendix C Euler's Gamma: Definition and Properties
Index