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Table of Contents
3.1 Concept of a Potential Well
3.2 The Infinite Potential Well
3.3 The Finite Potential Well
3.3.1 A Matrix Approach to the Finite Potential Well
3.4 Finite Potential Well-Even Solutions
3.5 Number of Bound States in a Finite Potential Well
3.6 Sketching Wavefunctions
3.7 Potential Barriers and Scattering
3.8 Penetration of Arbitrarily-Shaped Barriers
3.9 Alpha-Decay as a Barrier Penetration Effect
3.10 Scattering by One-Dimensional Potential Wells
References
4 Operators, Expectation Values, and Various Quantum Theories
4.1 Properties of Operators
4.2 Expectation Values
4.3 The Uncertainty Principle
4.4 Commutators and Uncertainty Relations
4.5 Ehrenfest's Theorem
4.6 The Orthogonality Theorem
4.7 The Superposition Theorem
4.8 Constructing a Time-Dependent Wave Packet
4.9 The Virial Theorem
4.10 Momentum-Space Wavefunctions
References
5 The Harmonic Oscillator
5.1 A Lesson in Dimensional Analysis
5.2 The Asymptotic Solution
5.3 The Series Solution
5.4 Hermite Polynomials and Harmonic Oscillator Wavefunctions
5.5 Comparing the Classical and Quantum Harmonic Oscillators
7.3 The Finite Spherical Well
7.4 The Coulomb Potential
7.5 Hydrogen Atom Probability Distributions
7.5.1 The (1, 0, 0) State of Hydrogen
7.5.2 The (2, 0, 0) and Other States of Hydrogen
7.6 The Effective Potential
7.7 Some Philosophical Remarks
References
8 Further Developments with Angular Momentum and Multiparticle Systems
8.1 Angular Momentum Raising and Lowering Operators
8.2 The Stern-Gerlach Experiment: Evidence for Qunatized Angular ...
8.3 Diatomic Molecules and Angular Momentum
3.2 The Infinite Potential Well
3.3 The Finite Potential Well
3.3.1 A Matrix Approach to the Finite Potential Well
3.4 Finite Potential Well-Even Solutions
3.5 Number of Bound States in a Finite Potential Well
3.6 Sketching Wavefunctions
3.7 Potential Barriers and Scattering
3.8 Penetration of Arbitrarily-Shaped Barriers
3.9 Alpha-Decay as a Barrier Penetration Effect
3.10 Scattering by One-Dimensional Potential Wells
References
4 Operators, Expectation Values, and Various Quantum Theories
4.1 Properties of Operators
4.2 Expectation Values
4.3 The Uncertainty Principle
4.4 Commutators and Uncertainty Relations
4.5 Ehrenfest's Theorem
4.6 The Orthogonality Theorem
4.7 The Superposition Theorem
4.8 Constructing a Time-Dependent Wave Packet
4.9 The Virial Theorem
4.10 Momentum-Space Wavefunctions
References
5 The Harmonic Oscillator
5.1 A Lesson in Dimensional Analysis
5.2 The Asymptotic Solution
5.3 The Series Solution
5.4 Hermite Polynomials and Harmonic Oscillator Wavefunctions
5.5 Comparing the Classical and Quantum Harmonic Oscillators
7.3 The Finite Spherical Well
7.4 The Coulomb Potential
7.5 Hydrogen Atom Probability Distributions
7.5.1 The (1, 0, 0) State of Hydrogen
7.5.2 The (2, 0, 0) and Other States of Hydrogen
7.6 The Effective Potential
7.7 Some Philosophical Remarks
References
8 Further Developments with Angular Momentum and Multiparticle Systems
8.1 Angular Momentum Raising and Lowering Operators
8.2 The Stern-Gerlach Experiment: Evidence for Qunatized Angular ...
8.3 Diatomic Molecules and Angular Momentum