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Really sorry for this simple question, but I think it will be useful/interesting in general.

Consider a quantum simple harmonic oscillator. Add a perturbation $H_I = -\lambda \hat{x}$

Calculate $\langle \psi| \hat{x} |\psi \rangle$ in the new ground state, to first order in perturbation theory in $\lambda$, and relate it to $\langle 0| x^2 |0 \rangle $ where $| 0 \rangle$ is the unperturbed ground state.

Can someone help me on this

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Note that the homework tag "Applies to questions of primarily educational value - not only questions that arise from actual homework assignments (emphasis mine), but any question where it is preferable to guide the asker to the answer rather than giving it away outright." So where are you getting stuck? – Michael Brown Apr 4 '13 at 11:03
I think the Hellmann-Feynman theorem might be of use here. – Wouter Apr 4 '13 at 11:37

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