Massachusetts Institute of Technology

Department of Physics

Physics 8.04, Spring 1997February 5, 1997

Quantum Physics I, Spring 1997

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 (section numbers), G = Gasiorowicz (read section(s) contained with in given range of pages), H = Heisenberg (section numbers), FT = French and Taylor (section numbers), 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, H I2a]

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

• Classical E&M (recall)
• Photoelectric Effect (A Einstein) and related effects [RH 5.1-5.3, 5.6, G 9]
• Single slit experiments (GI Taylor)
• Poisson statistics [CN ``Statistics'']
• Compton Scattering [RH 5.4, H I2d, G 11]

3. Electrons

• JJ Thomson (recall)
• Davisson-Germer Interference [CN ``de Broglie,'' RH 6.2, H I2b-c, G 13-15]
• GP Thomson Interference

III. Exploration of Qualitative and Semiquantitative Pictures

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

B. Heisenberg Uncertainty Principle (HUP) [RH 6.5-6.7, CN ``HUP'', H II, G 33-38]

• Energy of the Hydrogen atom [CN ``HUP'']
• Atomic Spectra [RH 7.4]
• Franck-Hertz Experiment [RH 4.7, H I2e]

C. Semiclassical Quantization and the Correspondence Principle [CN ``Bohr-Sommerfeld,'' [RH 7.7, 7.5, G 15-21]

• X-ray Spectra (Moseley) [FT 1.10]

IV. Constructing a Quantitative Theory Consistent with the Experimental Evidence

A. ``Kinematics'': The Wavefunction/Operator Framework [H IV3]

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

2. Operators [CN ``Quantum Operators'', G 45-46, 114-118]

B. ``Dynamics'': Time-Dependent Schrödinger Equation (TDSE) [CN ``TDSE'', G 49-50]

1. Verify consistency with probabilistic interpretation: probability currents, [CN ``TDSE'', G 42-45]

2. Verify consistency with the correspondence principle: Ehrenfest's Theorem, [G 125-127]

3. Computer solutions as examples

V. 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'']

• Qualitative solutions (1d) [FT 3.11]

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

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

1. Wave packets [G 27-31]

• Gaussian packet
• General Packet and Stationary phase

2. Reflection at a step/time delay, [G 74-85, 86-89]

3. Feynman diagrams and sum over histories

4. Symmetry and resonance

B. Bound States in One Dimension

1. General features - eigenstate expansions, energy representation [CN ``TISE'', G 60-63]

2. Piecewise constant potentials [CN ``Finite Square Well'', [G 58, 67-70, 89-93]

3. -function potential [G 93-99]

4. Simple Harmonic Oscillator [CN ``SHO'', G 103-108]

• dimensional analysis
• momentum representation/self-transform property of solutions
• full power series solution

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