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Here's the question:

Consider a particle of mass 'm' in a one-dimensional infinite potential well of width 'a'

[tex]

V (x) = \left\{\begin{array}{c} 0 \ \ \ if \ \ \ 0 \leq x \leq a \\ \infty \ \ \ otherwise

[/tex]

The particle is subject to a perturbation of the form:

[tex]

\omega (x) = a \omega_0 \delta \left(x - \frac{a}{2} \right)

[/tex]

Where 'a' is a real constant with dimension of energy. Calculate the changes in the energy level of the particle in the first order of [itex] \omega_0 [/itex]

I just need some help starting off at this point. Can anyone suggest how to begin?