5.73 | Fall 2005 | Graduate

Introductory Quantum Mechanics I

Calendar

Lec # TOPICS KEY DATES
1-4

Experimental Evidence for Quantum Mechanics

Polarization of Light

Single Molecule Fluorescence

 
5-7

The Machinery of Quantum Mechanics

Hilbert Space

State Vectors

Bra-Ket

Operators and Eigenvalues

 
8-12

Exactly Solvable Problems

Operators and States in Real Space

Harmonic Oscillator

Position Representation and Wave Mechanics

Piecewise Constant Potentials

Problem set 1 due after Lec #8

Problem set 2 due after Lec #11

13-15

Matrix Mechanics

Vector Representation of States

Matrices as Operators

Interesting Matrix Properties

Discrete Variable Representation

Variational Method

Problem set 3 due after Lec #14

Problem set 4 due after Lec #17

16-18

Time Dependence

Energy Eigenstates and Stationary States

The Propagator

Time Dependence of Average Values

Matrix Representations of the Propagator

Example: Inversion of the Ammonia Molecule

Midterm exam handed out after Lec #18
19-20

Angular Momentum

Rotations

Commutation Relations

Eigenstates

 
21-22

Central Potentials

Spherical Polar Coordinates

Orbital Angular Momentum Operators

Spherical Harmonics

The Radial Equation

Hydrogen-like Atoms

Electron Spin

Midterm exam due after Lec #21
23-24

Addition of Angular Momenta

Coupled and Uncoupled Bases

Recursion Relations

The Triangle Rule

 
25

Wigner-Eckart Theorem

Spherical Tensors

 
26-28 Perturbation Theory Problem set 5 due after Lec #27
29-31

Identical Particles

The Product Basis

Symmetry Under Exchange

Two Electron Atoms

Hartree-Fock

Perturbation Theory

Configuration Interaction

Problem set 5 due after Lec #31
32-34

The Born-Oppenheimer Approximation

The Adiabatic Approximation

The Coupled Channel Hamiltonian

Non-Adiabatic Effects

Diabatic States

Electron Transfer

 
35-38

The Hydrogen Molecule

Minimal Atomic Orbital Basis

Molecular Orbital Picture

Valence Bond Picture

Problem set 7 due after Lec #35

Final exam after Lec #38

Course Info

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As Taught In
Fall 2005
Level
Learning Resource Types
Exams with Solutions
Lecture Notes
Problem Sets with Solutions