**Introduction to Quantum Mechanics I**

Physics 3372 SyllabusPhysics 3372 Syllabus

**Part I: Quantum Principals**

**Chapter 1: Perspective and Principles**

1.1 Failure of classical mechanics

1.2 Stern-Gerlach experiment

1.3 Idealized Stern-Gerlach results

1.4 Classical model attempts

1.5 Wave functions for two physical outcome case

1.6 Process diagrams, operators, and completeness

1.7 Further properties of operators/modulation

1.8 Operator reformulation

1.9 Operator rotation

1.10 Bra-ket notation/basis states

1.11 Transition amplitude

1.12 Three-magnet setup example/coherence

1.13 Hermitian conjugation

1.14 Unitary operators

1.15 A very special operato

1.16 Matrix representations

1.17 Matrix wave function recovery

1.18 Expectation values

1.19 Wrap up

Problems

**Chapter 2: Free Particles in One Dimension**

2.1 Photoelectric effect

2.2 Compton effect

2.3 Uncertainty relation for photons

2.4 Stability of ground states

2.5 Bohr model

2.6 Fourier transform and uncertainty relations

2.7 SchrÃ¶dinger equation

2.8 SchrÃ¶dinger equation example

2.9 Dirac delta functions

2.10 Wave functions and probability

2.11 Probability current

2.12 Time separable solutions

2.13 Completeness for particle states

2.14 Particle operator properties

2.15 Operator rules

2.16 Time evolution and expectation values

2.17 Wrap-up of Chapter 2

Problems

**Chapter 3: Some One-Dimensional Solutions to the Schrodinger Equation**

3.1 Introduction

3.2 The infinite square well: differential solution

3.3 The infinite square well: operator solution

3.4 The finite potential barrie

3.5 The harmonic oscillator

3.6 The attractive Kronig-Penney mode

3.7 Bound state and scattering solutions

Problems

**Chapter 4: More About Hilbert Space**

4.1 Introduction and notation

4.2 Hermitian conjugation/Inner and outer products

4.3 Operator-matrix relationship

4.4 Hermitian operators and eigenkets

4.5 Schmidt orthogonalization process

4.6 Compatible Hermitian operators

4.7 Uncertainty relations and incompatible observables

4.8 Simultaneously measurable operators

4.9 Unitary transformations and change of basis

4.10 Coordinate displacements and unitary transformation

4.11 Heisenberg picture of time evolution/Constants of the motion

4.12 Free Gaussian wave packet in Heisenberg pictur

4.13 Potentials and Ehrenfest theorem

Problems

**Chapter 5: Two Static Approximation Methods**

5.1 Introduction

5.2 Time-independent perturbation theory

5.3 Examples of time-independent perturbation theory

5.4 Aspects of degenerate perturbation theory

5.5 WKB semiclassical approximation

5.6 Use of WKB approximation in barrier penetration

5.7 Use of WKB approximation in bound states

5.8 Variational methods

Problems

**Chapter 6: Generalization to Three Dimensions**

6.1 Cartesian basis states and wave functions in three dimensions

6.2 Position/momentum eigenstate generalization

6.3 Example: Three dimensional infinite square well

6.4 Spherical basis states

6.5 Orbital angular momentum operator

6.6 Effect of angular momentum on basis states

6.7 Energy eigenvalue equation and angular momentum

6.8 Complete set of observables for the radial Schrodinger equation

6.9 Specification of angular momentum eigenstates

6.10 Angular momentum eigenvectors and spherical harmonics

6.11 Completeness and other properties of spherical harmonics

6.12 Radial eigenfunctions

Problems