For the harmonic oscillator [tex]V(x) = \frac{1}{2}kx^2[/tex], the allowed energies are [tex]E_n=(n+1/2)h \omega[/tex] where [tex]\omega = \sqrt{k/m}[/tex] is the classical frequency. Now suppose the spring constant increases slightly: k -> [tex](1 + \epsilon)k[/tex]. Calculate the first order perturbation in the energy.(adsbygoogle = window.adsbygoogle || []).push({});

This is 6.2 from Griffith' s book and after this question he gives the following hint although according to me, the hint is more confusing than the question without the hint:

Hint

What is H' here? It is not necessary- in fact it is not permitted - to calculate a single integral in doing this problem.

I understand what the formula looks like..it is

[tex]E_n^1 = <\psi_n^0 |H'| \psi_n^0>[/tex]

but how can this be done without evaluating a single integral? Also what is H' ?

James

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# Homework Help: Perturbation theory

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