Massachusetts Institute of Technology

Department of Physics

Physics 8.04 Thu Oct 12 16:34:00 EDT 1995

Quantum Physics I, Spring 1995

Note: The notations in square brackets give chapter and section readings roughly corresponding to the material in the outline. The abbreviations are FT = ``French and Taylor'' ER = ``Eisberg and Resnick,'' and FLP = ``Feynman Lectures in Physics.''

Many thanks to Charles Sestok (U'97) and Jason Strautman (U'97) for their help, which was invaluable in the production of this syllabus.

Syllabus

I. Overview: Following the Scientific Method

II. The Experimental Evidence

A. Identity of the Basic Building Blocks of the World Around Us [FT 1.1-1.5]

1. Electrons (JJ Thomson/RA Millikan)

2. Nuclei (E. Rutherford)

3. Electromagnetic Energy/Radiation (comment)

B. Behavior of the Building Blocks [FT 1.6; ER Ch. 1; FLP Ch. 1 & 2]

1. Nuclei (comment)

2. Electromagnetic Energy

Black Body Radiation (M. Planck) [ER 1.2-1.4, 1.6 (1.5, 1.7)]

Photoelectric Effect (A. Einstein) [FT 1.6]

Compton Scattering [FT 1.6]

3. Electrons [FT, Ch. 2; FLP Ch. 1 and 2]

de Broglie Hypothesis

interference (Davisson-Germer)

probability amplitudes

Heisenberg uncertainty principle

C. Combining the Building Blocks: Atoms [FT 1.7-1.10]

1. Bohr Picture

2. Franck-Hertz Experiment

3. X-ray Spectra (Moseley)

4. Semiclassical Quantization and the Correspondence Principle

D. Review of Phenomena which a Quantum Theory Must Describe

III. Constructing a Theory Consistent with the Experimental Evidence [class notes]

A. ``Kinematics'': The Wavefunction/Operator Framework

1. Wavefunctions/Fourier Transforms

2. Operators

3. Verify consistency of framework with uncertainty principle

B. ``Dynamics'': Time-Dependent Schrödinger Equation (TDSE)

1. Verify consistency with probabilistic interpretation: probability currents

2. Verify consistency with the correspondence principle: Ehrenfest's Theorem

3. Computer solutions

IV. Tools to Apply the Theory: Solving the TDSE

A. Separation of Variables: Reduction to Time-Independent Schrödinger Equation ( TISE)

1. Example: detailed analysis of a wave packet in free space

B. Time Independent Schrödinger Equation

1. General features

variational principle

general virial theorem

2. Qualitative solutions (1d)/WKB Approximation [FT 3.11]

3. Analytic solutions (1d)/Transfer Matrix Method [FT 3.5, 4.2]

V. Predictions of the Theory: Solutions to Schrödinger's Equation

A. Bound States in One Dimension [FT, Ch. 4]

1. Piecewise constant potentials

2. Simple Harmonic Oscillator

dimensional analysis

momentum representation

B. Scattering States in One Dimension

1. Reflection at a step

2. Tunneling through a wall/WKB revisited

C. Metastable States

1. Resonant tunneling through a double wall

D. Beyond One Dimension: Solutions in Central Potentials

1. Separation of variables, angular wavefunctions and Spherical Harmonics

2. Atomic States: solutions to the radial equation

VI. Survey of Alternate Formulations of Quantum Mechanics (Time permitting)

A. Feynman Sum over Histories: Scattering in One Dimension Made Easy

B. Operator Mechanics: the Simple Harmonic Oscillator Made Easy

C. Density Functional Theory: Multiple Electron Systems Made Easy

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