Write down an explicit formula for the second-order perturbation contribution to the ground state energy in exercise 2 , without calculating the terms and summing them.

Data From Exercise 2:-

Consider a hydrogenoid atom perturbed by a decaying exponential potential \(\lambda \hat{H}_{1}=\lambda e^{-\mu r}\). Calculate the first-order perturbation theory corrections to the energy and ground state wave function.