In quantum mechanics, there is a method to find approximations to the ground state and some excited states of an atom. The method requires one to use a "trial" function of some parameter and calculate the value of these parame- ters for which the expectation value of the energy is minimum. Let the trial function be: P(a) = Ae-ar To calculate the expectation value, one needs to find the inner product of the trial function with the Hamiltonian (i.e. Total energy) acting on itself, as defined by: | $(a)HÞ(a}r°dr Using gamma function, calculate the potential term of the inner product in terms of A, a, e, and eo: A?e? re-2ar dr 4neo

In quantum mechanics, there is a method to find approximations to the ground state and some excited states of an atom. The method requires one to use a "trial" function of some parameter and calculate the value of these parame- ters for which the expectation value of the energy is minimum. Let the trial function be: P(a) = Ae-ar To calculate the expectation value, one needs to find the inner product of the trial function with the Hamiltonian (i.e. Total energy) acting on itself, as defined by: | $(a)HÞ(a}r°dr Using gamma function, calculate the potential term of the inner product in terms of A, a, e, and eo: A?e? re-2ar dr 4neo