1. 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

3. 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

4. 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

5. 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

7. 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