Who can solve the probability of perturbation in simple harmonic oscillator

[Youngwoo]

Pleae help me.
a),b),c) was already solved.
but question d) is not.

 

[Tangent87]

I'm not 100% sure but maybe you have to find an expression for the perturbed wavefunction in the ground state and then use this to find the probability? Again, that is just my intuition, I may be completely wrong, but I'd be interested to see a solution.

Also just out of interest how did you do part (i)? I assume you use normalisation to find N, but how do you find alpha?

 

[Youngwoo]

I'm not 100% sure but maybe you have to find an expression for the perturbed wavefunction in the ground state and then use this to find the probability? Again, that is just my intuition, I may be completely wrong, but I'd be interested to see a solution.

Also just out of interest how did you do part (i)? I assume you use normalisation to find N, but how do you find alpha?

I attached my solution