When dealing with the harmonic oscillator, we discussed the virial theorem. This states that for a system with
potential energy of the form V (r) = αrs the expectation value for the kinetic energy <T> and the potential energy <V> follow 2<T> = s<V>. Applying the virial theorem to the H atom:
(a) Does the potential energy for the H atom fulfill the conditions for the virial theorem to hold?
(b) Write down the result of the virial theorem to the H atom.
(c) Check the virial theorem for the H atom explicitly for the ground state, i.e. the state with quantum numbers n = 1, l = 0, m = 0. Evaluate the expectation value of the kinetic and potential energy explicitly
(a) Yes, the potential energy for the H atom, fulfills the conditions of the virial theorem.... View the full answer