Determine the ground state energy to first-order in epsilon

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Reference no: EM13553448

A particle of mass m is confined to move in a one-dimensional "infinite" potential well defined by V(x)=0, |x|< or=a, V(x)=infinity otherwise. The energy eigenvalues are E(subscript n)=((n^2)(pi^2)(h-bar^2))/(8m a^2), with n=1,2,3,... and the orthonormal eigenfunctions are the even and odd functions

psi(subscript n)=
[1/(sqrt a)]cos(n pi x/2a) for n=1, 3, 5...
[1/(sqrt a)]sin(n pi x/2a) for n=2, 4, 6 ...

The potential is modified between -a<x<a to V(x)=epsilon[(pi^2)(h-bar^2)/(8ma^2)]sin((3pi x)/2a) with epsilon<1

a) Determine the ground state energy to first-order in epsilon. (Note 2 sin Acos B=sin(A+B)+sin(A-B))

Reference no: EM13553448

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