Physics · Quantum Mechanics

The normalized eigenstates of a particle in a one-dimensional potential well V(x) = 0 for 0 ≤ x ≤ a, and ∞ otherwise, are given by ψn(x) = √2a sin(nπxa), where n = 1, 2, 3, ... . The particle is subjected to a perturbation V'(x) = V0 cos(πxa) for 0 ≤ x ≤ a/2, and 0 otherwise. If the shift in the ground state energy due to the perturbation in the first-order perturbation theory is αV0, then the value of α is: