Quantum Mechanics I

Lecture Notes

ses #	topics
1–9: One-Dimensional Problems
1	Course Outline; Free Particle; Motion (PDF)
2	Infinite Box, \(\delta(x)\) Well, \(\delta(x)\) Barrier (PDF - 1.0MB)
3	Probability Density: Motion, Position, Spreading, Gaussian Wavepacket (PDF - 1.6MB)
4	Stationary Phase and Gaussian Wavepackets (PDF)
5	Continuum Normalization (PDF)
6	Linear Potential; JWKB Approximation and Quantization (PDF - 1.4MB)
7	JWKB Quantization Condition (PDF - 1.1MB)
8	Rydberg-Klein-Rees: \(V(x)\) from \(E_{vJ}\)(PDF - 1.4MB)
9	Numerov-Cooley Method: 1-D Schrödinger Equation (PDF)
10–19: Matrix Mechanics
10	Matrix Mechanics (PDF - 1.1MB)
11	Eigenvalues, Eigenvectors, and Discrete Variable Representation (PDF - 1.1MB)
12	Matrix Solution of Harmonic Oscillator I (PDF - 1.1MB)
13	Matrix Solution of Harmonic Oscillator II (PDF - 1.3MB)
14	Perturbation Theory I (PDF - 1.2MB)
15	Perturbation Theory II (PDF - 1.2MB)
16	Perturbation Theory III (PDF - 1.2MB)
17	Perturbation Theory IV (PDF - 1.1MB)
18	Variational Method (PDF)
19	Density Matrices I (PDF)
20–29: Central Forces and Angular Momentum
20	Density Matrices II (PDF - 1.0MB)
21	3-D Central Force Problems I (PDF - 1.5MB)
22	3-D Central Force Problems II (PDF - 1.6MB)
23	Angular Momentum Matrix Elements from Commutation Rules (PDF)
24	J-Matrices (PDF - 1.3MB)
25	H{{< sup “SO” >}} + H{{< sup “Zeeman” >}}: Coupled vs. Uncoupled Basis Sets (PDF - 1MB)
26	H{{< sup “SO” >}} + H{{< sup “Zeeman” >}} in ⎜JLSM{{< sub “J” >}}(rangle) and ⎜LM{{< sub “L” >}}M{{< sub “S” >}}(rangle) by Ladders plus Orthogonality (PDF)
27	Wigner-Eckart Theorem (PDF - 1.2MB) Lecture 27 Supplement 1: Angular Momentum Eigenvalues (PDF) (Courtesy of Dudley Herschbach. Used with permission.) Lecture 27 Supplement 2: Simplification of hyperfine H{{< sup “hf” >}} by Wigner-Eckart Theorem (PDF) Lecture 27 Supplement 3: A User’s Guide to Angular Momentum Theory (PDF - 2.2MB)
28	Hydrogen Radial Wavefunctions (PDF - 1.1MB)
29	Begin Many-Electron Atoms: Quantum Defect Theory (PDF - 1.0MB)
30–39: Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice
30	Matrix Elements of Many-Electron Wavefunctions (PDF - 1.3MB)
31	Matrix Elements of One-Electron, \(F(i)\), and Two-Electron, \(G(i,j)\) Operators (PDF - 1.2MB)
32	Configurations and Resultant L–S–J States (PDF - 1.4MB)
33	L-S Terms via L{{< sup “2” >}}, S{{< sup “2” >}} and Projection (PDF - 1.0MB)
34	\(e^2/r_{ij}\) and Slater Sum Rule Method (PDF - 1.3MB)
35	Spin Orbit: Many Electron ζ(N,L,S)↔Single Orbital ζ\(_{nl}\) Coupling Constants (PDF - 1.2MB)
36	Holes; Hund’s Third Rule; Landé g-Factor via W-E Theorem (PDF)
37	Infinite 1-D Lattice I (PDF - 1.0MB)
38	Infinite 1-D Lattice II (PDF - 1.1MB)
39	One-Dimensional Lattice: Weak-Coupling Limit (PDF - 1.0MB)