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Problem #4 - 20 PTS → Evaluate the first order correction to the energy of the...

Question:

Problem #4 - 20 PTS → Evaluate the first order correction to the energy of the nth state of one-dimensional harmonic oscillat

Problem #4 - 20 PTS → Evaluate the first order correction to the energy of the nth state of one-dimensional harmonic oscillator having the potential energy V = mox? + bx*, where bx* « mox? using raising and lowering operators At and A. Remember x = ( '(A+ A+). 11/2

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Given perturbation, H=bx4 where, * below 2 A++*+) 2 mw ::x= [(A+++ (a*%+2 AA] (A- A+ = ( ) zinte [ (A+)**(**)*+2. ] - [14]++Now, the first order correction in the nth energy level is E) = (n Hlln) z (nIbx4 in) = (npb 62 (2 + a)n) using, Atiny = cIn

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