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Non-degenerate perturbation theory
Quantum II (PHYS 4410) Lecture 9 Non-degenerate perturbation theory © Chuck Rogers, 2014 HWK 3 due Wed. 5PM HWK 1 scores and comments on D2L
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State vectors for the simple harmonic oscillator (1-d) are:
Always products of decaying exponentials and Laguerre polynomials Always products of Gaussians and Hermite polynomials. Neither of these. INSTRUCTOR NOTES: (Rogers) C. Neither of these, because a state vector can always be a linear superposition of arb. Basis vectors. Trying to drive home this general idea that general state vectors are written as linear superpositions of (your choice of) basis vectors. USED IN: Rogers, Sp12, L43, 0% 0% 0% 0% 0% CORRECT ANSWER: C WRITTEN BY: Chuck Rogers (CU-Boulder) 150 3
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The energy eigen state vectors for the simple harmonic oscillator (1-d) are:
Always represented as products of decaying exponentials and Laguerre polynomials Always represented as products of Gaussians and Hermite polynomials. Neither of these. INSTRUCTOR NOTES: (Rogers) C. Neither of these, because the representation is always a CHOICE. In the cases of the energy eigen state vectors for the harmonic oscillator, we can also use a representation |n> labeled by the quantum number and with known behavior with raising and lower operators, etc. USED IN: Rogers, Sp12, L43, 0% 0% 0% 0% 0% CORRECT ANSWER: C WRITTEN BY: Chuck Rogers (CU-Boulder) 150 4
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The energy eigen values of the simple harmonic oscillator (1-d) are given by:
Something else INSTRUCTOR NOTES: (Rogers) C. Tempted to be mean and change the n condition to match the others… USED IN: Rogers, Sp12, L43, 0% 0% 0% 0% 0% CORRECT ANSWER: C WRITTEN BY: Chuck Rogers (CU-Boulder) 150 5
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Given a constant small potential, V0, the first order energy shift predicted by 1st order non-degenerate perturbation theory is: A) 0 B) Depends on details of C) Something else INSTRUCTOR NOTES: (Rogers) C. The constant value factors out. The rest is due to orthonormality of the original energy eigen states. USED IN: Rogers, Sp12, L43, 0% 0% 0% 0% 0% CORRECT ANSWER: C WRITTEN BY: Chuck Rogers (CU-Boulder) 150 7
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