# HW6 - done in class 3 Griﬃths’ Problem 6.4 Check that...

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Quantum Mechanics II, Physics 4143: Assignment 6, Spring 2011. Nondegenerate perturbation theory examples. 1 : Griﬃths’ Problem 6.2 Harmonic oscillator: you may need to review the properties of ˆ a and ˆ a operators from QM I, e.g. ˆ au n = nu n - 1 ; ˆ a u n = n + 1 u n +1 . Remember the raising and lowering operators are very useful in evaluating matrix elements algebraically - just what is needed in perturbation theory. 2 : Griﬃths’ Problem 6.3 Interacting bosons. Fill in the details from the worked example
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Unformatted text preview: done in class. 3 : Griﬃths’ Problem 6.4 Check that you can indeed follow the perturbation theory recipes. Summing the inﬁnite series explicitly is made possible by using a trick based on the partial fractions expansion 1 n 2-m 2 = 1 2 n ( 1 m + n-1 m-n ) 4 : Griﬃths’ Problem 6.5 Charged oscillator in a ﬁeld. We solved part (b) in class. Please do the perturbation theory in part (a) and compare. 1...
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