Physics 443: Quantum Mechanics I
Midterm Exam I: 12:30–13:45 Thursday 8 February 2018 in SA124a for seventy-five (75) minutes.
This is a closed-book examination. No calculators are permitted.
Answer fully five (5) of the eight (8) questions. Cross out solutions you do not want marked,
or else only your first five (5) answers are marked if you complete more than five (5).
All questions have equal value. Answers must be written in the test booklets provided.
1. Explain what a symplectic manifold is including specific mention of each of its properties, and show that the cross
product satisfies the properties of the symplectic bilinear form.
2. Explain the Poisson bracket {•,•}, and write the mathematical identities that the Poisson bracket satisfies.
3. Explain mathematically what a conservative classical system is, and write the Liouville operator for this case.
4. What is the essential principle of classical mechanics, and which experimental phenomena hinted at the breakdown
of this principle, thereby ushering in Old Quantum Theory?
5. Write Sommerfeld’s quantized-action conditions.
6. Discuss Bohr’s two postulates of Old Quantum Theory.
7. Explain the principle of classical-quantum correspondence.
8. Explain the principle of complementarity.
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