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EbookNice Team
Status:
Available5.0
13 reviews
ISBN 10: 981024634X
ISBN 13: 9789810246341
Author: Anton Z Capri
The main unique feature of Nonrelativistic Quantum Mechanics is its discussion of Hilbert space and rigged Hilbert space. This invaluable book is suitable for advanced undergraduate students as well as graduate students.
1 The Breakdown of Classical Mechanics
1.1 Introduction
1.2 Blackbody Radiation
1.3 Stability of Atoms: Discrete Spectral Lines
1.4 Photoelectric Effect
1.5 Wave Particle Duality
1.5.1 Reflection
1.5.2 Refraction
1.6 de Broglie's Hypothesis
1.7 The Compton Effect
1.8 The Davisson-Germer Experiment
1.9 The Franck-Hertz Effect
1.10 Planck's Radiation Law
1.11 Einstein's Model for Specific Heat
1.12 The Debye Model
1.13 Bohr Model and the Hydrogen Atom
1.14 Problems
2 Review of Classical Mechanics
2.1 Introduction
2.2 Classical Mechanics: Particle in One Dimension
2.3 Lagrangian and Hamiltonian Formulation
2.4 Contact Transformations: Hamilton-Jacobi Theory
2.5 Interpretation of Action-Angle Variables
2.6 Hydrogen Atom: Bohr-Sommerfeld Quantization
2.7 The Schrodinger Equation
2.8 Problems
3 Elementary Systems
3.1 Introduction
3.2 Plane Wave Solutions
3.3 Conservation Law for Particles
3.4 Young's Double Slit Experiment
3.5 The Superposition Principle and Group Velocity
3.6 Formal Considerations
3.7 Ambiguities
3.7.1 Use of Different Coordinate Systems
3.7.2 Non-Commutativity
3.8 Interaction with an Electromagnetic Field
3.9 Problems
4 One-Dimensional Problems
4.1 Introduction
4.2 Particle in a Box
4.3 Parity
4.4 Scattering from a Step-Function Potential
4.4.1 Boundary Conditions
4.4.2 Particles from the Left
4.4.3 Interpretation of R and S
4.5 Finite Square Well: Bound States
4.6 Tunneling Through a Square Barrier
4.6.1 Resonance Transmission
4.7 Time Reversal
4.8 Problems
5 More One-Dimensional Problems
5.1 Introduction
5.2 General Considerations
5.3 The Simple Harmonic Oscillator
5.3.1 Generating Function for Hermite Polynomials
5.3.2 Rodrigues Formula for Hermite Polynomials
5.3.3 Normalization
5.4 The Delta Function
5.5 Attractive Delta Function Potential
5.6 Repulsive Delta Function Potential
5.7 Square Well: Scattering and Phase Shifts
5.8 Periodic Potentials .
5.8.1 Floquet's Theorem
5.8.2 Bloch's Theorem
5.9 The Kronig-Penney Problem
5.10 Problems
6 Mathematical Foundations
6.1 Introduction
6.2 Geometry of Hilbert Space
6.3 L2- A Model Hilbert Space
6.4 Operators on Hilbert Space: Mainly Definitions
6.5 Cayley Transform: Self-Adjoint Operators
6.6 Some Properties of Self-Adjoint Operators
6.7 Classification of Symmetric Operators
6.8 Spontaneously Broken Symmetry
6.9 Problems
7 Physical Interpretation
7.1 Introduction
7.2 A1 - Physical States
7.3 A2 - Observables
7.4 A3 - Probabilities
7.5 A4 - Reduction of the Wave Packet
7.5.1 Example
7.6 Compatibility Theorem and Uncertainty Principle
7.7 The Heisenberg Microscope
7.8 A5 - The Schrodinger Equation
7.9 Time Evolution: Constants of the Motion
7.10 Time-Energy Uncertainty Relation
7.11 Time Evolution of Probability Amplitudes
7.12 Problems
8 Distributions and Fourier Transforms
8.1 Introduction
8.2 Functionals
8.3 Fourier Transforms
8.4 Rigged Hilbert Spaces
8.5 Problems
9 Algebraic Methods
9.1 Introduction
9.2 Simple Harmonic Oscillator
9.2.1 Expectation Values
9.3 The Rigid Rotator
9.4 3D Rigid Rotator: Angular Momentum
9.5 Algebraic Approach to Angular Momentum
9.6 Rotations and Rotational Invariance
9.7 Spin Angular Momentum
9.8 Problems
10 Central Force Problems
10.1 Introduction
10.2 The Radial Equation
10.3 Infinite Square Well
10.4 Simple Harmonic Oscillator: Cartesian Coordinates
10.4.1 Degeneracy
10.5 Simple Harmonic Oscillator: Spherical Coordinates
10.6 The Hydrogenic Atom
10.6.1 Laguerre Polynomials
10.7 Reduction of the Two-Body Problem
10.8 Problems
11 Transformation Theory
11.1 Introduction
11.2 Rotations in a Vector Space
11.2.1 Fourier Transform of Hermite Functions
11.3 Dirac Notation
11.4 Coherent States
11.4.1 The Forced Simple Harmonic Oscillator
11.5 Quasi-classical States
11.6 Squeezed States
11.7 Example: Angular Momentum
11.8 Schrodinger Picture
11.9 Heisenberg Picture
11.10 Dirac or Interaction Picture
11.11 Hidden Variables
11.12 Problems
12 Non-Degenerate Perturbation Theory
12.1 Introduction
12.2 Rayleigh-Schrodinger Perturbation Theory
12.3 First Order Perturbations
12.4 Anharmonic Oscillator
12.5 Ground State of Helium-like Ions
12.6 Second Order Perturbations
12.7 Displaced Simple Harmonic Oscillator
12.8 Non-degenerate Perturbations to all Orders
12.9 Sum Rule: Second Order Perturbation
12.10 Linear Stark Effect
12.11 Problems
13 Degenerate Perturbation Theory
13.1 Introduction
13.2 Two Levels: Rayleigh-Schrodinger Method
13.3 Rayleigh-Schrodinger: Degenerate Levels
13.4 Example: Spin Hamiltonian
13.4.1 Exact Solution
13.4.2 Rayleigh-Schrodinger Solution
13.5 Problems
14 Further Approximation Methods
14.1 Introduction
14.2 Rayleigh-Ritz Method
14.3 Example: Simple Harmonic Oscillator
14.4 Example: He Ground State
14.5 The WKB Approximation
14.5.1 Turning points
14.6 WKB Applied to a Potential Well
14.6.1 Special Boundaries
14.7 WKB Approximation for Tunneling
14.8 Alpha Decay
14.8.1 Heuristic Discussion
14.8.2 Detailed Analysis
14.9 Problems
15 Time-Dependent Perturbation Theory
15.1 Introduction
15.2 Formal Considerations
15.3 Transition Amplitudes
15.4 Time-Independent Perturbation
15.5 Periodic Perturbation of Finite Duration
15.6 Photo-Ionization of Hydrogen Atom
15.7 The Adiabatic Approximation
15.8 The Sudden Approximation
15.9 Dipole in a Time-Dependent Magnetic Field
15.9.1 Oscillatory Perturbation
15.9.2 Slowly Varying Perturbation
15.9.3 Sudden Approximation
15.10 Two-Level Systems
15.11 Berry's Phase
15.12 Problems
16 Particle in a Uniform Magnetic Field
16.1 Introduction
16.2 Gauge Transformations
16.3 Motion in a Uniform Magnetic Field
16.3.1 Classical Hall Effect
16.3.2 Landau Levels
16.4 Crossed Electric and Magnetic Fields
16.4.1 The Quantum Hall Effect
16.5 Magnetic Field: Heisenberg Equations
16.6 Energy Eigenfunctions
16.7 Translation Invariant States
16.8 Gauge Transformations
16.9 Problems
17 Applications
17.1 Introduction
17.2 Spin and Spin-Orbit Coupling
17.3 Alkali Spectra
17.4 Addition of Angular Momenta
17.5 Two Spin 1/2 States
17.6 Spin 1/2 + Orbital Angular Momentum
17.7 The Weak-Field Zeeman Effect
17.8 The Aharonov-Bohm Effect
17.9 Problems
18 Scattering Theory - Time Dependent
18.1 Introduction
18.2 Classical Scattering Theory
18.3 Asymptotic States: Schrodinger Picture
18.4 The Moller Wave Operators
18.5 Green's Functions and Propagators
18.6 Integral Equations for Propagators
18.7 Cross-Sections
18.8 The Lippmann-Schwinger Equations
18.9 The S-Matrix and the Scattering Amplitude
18.10 Problems
19 Scattering Theory - Time Independent
19.1 Introduction
19.2 The Scattering Amplitude
19.3 Green's Functions
19.4 The Born Approximation
19.5 The Yukawa Potential
19.6 Free Particle in Spherical Coordinates
19.7 Partial Wave Analysis
19.8 Phase Shifts
19.9 The Optical Theorem: Unitarity Bound
19.10 Partial Waves: Lippmann-Schwinger Equation
19.11 Effective Range Approximation
19.12 Resonant Scattering
19.13 Problems
20 Systems of Identical Particles
20.1 Introduction
20.2 Two Identical Particles
20.3 The Hydrogen Molecule
20.4 N Identical Particles
20.5 Non-Interacting Fermions
20.6 Non-Interacting Bosons
20.7 N-Space: Second Quantization for Bosons
20.8 N-Space: Second Quantization for Fermions
20.9 Field Operators in the Schrodinger Picture
20.10 Representation of Operators
20.11 Heisenberg Picture
20.12 Problems
21 Quantum Statistical Mechanics
21.1 Introduction
21.2 The Density Matrix
21.2.1 The Microcanonical Ensemble
21.2.2 The Canonical Ensemble
21.2.3 The Grand Canonical Ensemble
21.3 The Ideal Gases
21.4 General Properties of the Density Matrix
21.5 The Density Matrix and Polarization
21.6 Composite Systems
21.7 von Neumann's Theory of Measurement
21.8 Decoherence
21.9 Conclusion
21.10 Problems
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Tags: Anton Z Capri, Nonrelativistic, Mechanics
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