Question: A simple harmonic oscillator (in one dimension) is subjected to a perturbation ?H1 = bx where b is a real constant. a. Calculate the energy

A simple harmonic oscillator (in one dimension) is subjected to a perturbation ?H1 = bx where b is a real constant.

a. Calculate the energy shift of the ground state to lowest non-vanishing order.

b. Solve this problem exactly and compare with your result obtained in (a). [You may assume without proof

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(Vn +18,. - ("n|x|"n> +1+ Vn 8 -1). "'.n+1

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