Change in ground state energy due to perturbation

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1. Apr 1, 2016

Shelly1

1. The problem statement, all variables and given/known data
Consider a quantum particle of mass m in one dimension in an infinite potential well , i.e V(x) = 0 for -a/2 < x < a/2 , and V(x) =∞ for |x| ≥ a/2 . A small perturbation V'(x) =2ε|x|/a , is added. The change in the ground state energy to O(ε) is:

2. Relevant equations
The ground state wave function for a particle an symmetric potential well is Ψ=√(2/a) cos(πx/a)
change in energy= <Ψ| V'(x) |Ψ>
3. The attempt at a solution
change in ground state energy can be calculated using this equation <Ψ| V'(x) |Ψ>

2. Apr 1, 2016

Shelly1

The correct answer to this question is ε(π^2 -4)/ 2π^2. I don't know how they got this.

3. Apr 1, 2016

Staff: Mentor

Have you tried calculating <Ψ| V'(x) |Ψ>?

4. Apr 1, 2016

Shelly1

Yes.but I got zero as answer.

5. Apr 1, 2016

Staff: Mentor

Were you careful to consider that it is |x| that appears in the potential?

6. Apr 1, 2016

Shelly1

Yes ofcourse...

7. Apr 1, 2016