5.73 | Fall 2005 | Graduate

Introductory Quantum Mechanics I

Lecture Notes

Lec # TOPICS
1-4 Experimental Evidence for Quantum Mechanics (PDF)

Polarization of Light

Single Molecule Fluorescence

5-7 The Machinery of Quantum Mechanics (PDF)

Hilbert Space

State Vectors

Bra-Ket

Operators and Eigenvalues

8-12 Exactly Solvable Problems (PDF)

Operators and States in Real Space

Harmonic Oscillator

Position Representation and Wave Mechanics

Piecewise Constant Potentials

13-15 Matrix Mechanics (PDF)

Vector Representation of States

Matrices as Operators

Interesting Matrix Properties

Discrete Variable Representation

Variational Method

16-18 Time Dependence (PDF)

Energy Eigenstates and Stationary States

The Propagator

Time Dependence of Average Values

Matrix Representations of the Propagator

Example: Inversion of the Ammonia Molecule

19-20 Angular Momentum (PDF)

Rotations

Commutation Relations

Eigenstates

21-22 Central Potentials (PDF)

Spherical Polar Coordinates

Orbital Angular Momentum Operators

Spherical Harmonics

The Radial Equation

Hydrogen-like Atoms

Electron Spin

23-24 Addition of Angular Momenta (PDF)

Coupled and Uncoupled Bases

Recursion Relations

The Triangle Rule

25 Wigner-Eckart Theorem (PDF)

Spherical Tensors

26-28 Perturbation Theory (PDF)
29-31 Identical Particles (PDF)

The Product Basis

Symmetry Under Exchange

Two Electron Atoms

Hartree-Fock

Perturbation Theory

Configuration Interaction

32-34 The Born-Oppenheimer Approximation (PDF)

The Adiabatic Approximation

The Coupled Channel Hamiltonian

Non-Adiabatic Effects

Diabatic States

Electron Transfer

35-38 The Hydrogen Molecule (PDF)

Minimal Atomic Orbital Basis

Molecular Orbital Picture

Valence Bond Picture

Course Info

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