An electron is moving freely inside a one-dimensional infinite potential well with walls at x = 0 and x = a. The size of the box is quadrupled suddenly. Consider that the particle is in nth quantum state initially before perturbation. Obtain an expression for the the probability of finding the particle in the mth state of the second well. Simplify the expression for the following cases: (i) m and n are odd integers (ii) m is even and n is odd (iii) m = n =1 (iv) n=1 and m=2

An electron is moving freely inside a one-dimensional infinite potential well with walls at x = 0 and x = a. The size of the box is quadrupled suddenly. Consider that the particle is in nth quantum state initially before perturbation. Obtain an expression for the the probability of finding the particle in the mth state of the second well. Simplify the expression for the following cases: (i) m and n are odd integers (ii) m is even and n is odd (iii) m = n =1 (iv) n=1 and m=2