Massachusetts Institute of Technology

Department of Physics

Physics 8.04, Spring 1996 Tue Feb 6 22:07:52 EST 1996

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 RH = Resnick and Halliday, K = Kroemer, FT = French and Taylor, CN = class notes given out in lecture and provided on the web.

Many thanks to Dicle Yesilleten (U'97) for her 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

1. Electrons (JJ Thomson/RA Millikan) [FT 1.3-1.4]

2. Nuclei (E. Rutherford) [RH 7.1-7.3]

3. Electromagnetic Energy/Radiation (comment)

B. Behavior of the Building Blocks

1. Nuclei (comment)

2. Electromagnetic Energy

Photoelectric Effect (A Einstein) and related effects [RH 5.1-5.3, 5.6]

Two slit experiments (GI Taylor) [CN ``Statistics,'' K 1.2.3]

Compton Scattering [RH 5.4]

3. Electrons

de Broglie Hypothesis [CN ``de Broglie'']

Interference (Davisson-Germer) [CN ``de Broglie,'' RH 6.2]

Two slit thought experiments [RH 6.4]

Probability amplitudes

Heisenberg Uncertainty Principle (HUP) [RH 6.5, CN ``HUP'']

C. Combining the Building Blocks: Atoms

1. Atomic Spectra [RH 7.4]

2. Bohr Picture [RH 7.3, 7.6]

3. Franck-Hertz Experiment [RH 4.7]

4. X-ray Spectra (Moseley) [FT 1.10]

5. Semiclassical Quantization and the Correspondence Principle [CN ``Bohr-Sommerfeld,'' RH 7.7, 7.5]

D. Review of Phenomena which a Quantum Theory Must Describe [K 1.1-1.2]

III. Constructing a Theory Consistent with the Experimental Evidence

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

1. Wavefunctions/Fourier Transforms [CN ``States and Observables'']

2. Operators [CN ``Quantum Operators,'' K 7.1 (1.3.3)]

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

1. Verify consistency with probabilistic interpretation: probability currents, [CN ``TDSE,'' K 1.5]

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

3. Computer solutions as examples

IV. Tools to Apply the Theory: Solving the TDSE

A. Separation of Variables: Reduction to Time-Independent Schrödinger Equation (TISE) [CN ``TISE'']

B. Time Independent Schrödinger Equation [CN ``TISE'']

1. General features -- eigenstate expansions, variational principle [CN ``TISE,'' K 1.4.1-1.4.2, 2.1]

2. Qualitative solutions (1d) [FT 3.11]/WKB Approximation [K 6.1]

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

A. Bound States in One Dimension

1. Piecewise constant potentials [CN ``Finite Square Well'', K 2.2.1, 2.2.3]

2. Simple Harmonic Oscillator [CN ``SHO,'' K 2.3.1-2.3.4]

dimensional analysis

momentum representation/self-transform property of solutions

full power series solution

B. Scattering States in One Dimension [CN ``Scattering'']

1. Wave packets in free space [K 4]

Gaussian packet [K 4.2]

Stationary phase

2. Reflection at a step/time delay [K 1.4.3]

3. Feynman sum over histories: resonant scattering from a well [K 5.3]

( **Application of an alternate formulation of Quantum Mechanics** )

4. Metastable States: Resonant tunneling through a double wall

C. Beyond One Dimension: Solutions in Central Potentials

1. Separation of variables, angular wavefunctions and Spherical Harmonics [K 3.1]

2. Hydrogen Atom: solutions to the radial equation [K 3.2]

D. Beyond One Particle: Actual methods used in modern quantum calculations of complex systems (time permitting)

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