1. ‘When dealing with the harmonic oscillator, we discussed the yirial theorem. This
states that for a system with potential energy of the form V(r} = or” the expectation value for the kinetic energy (T) and the potential energy (V) follow 2d“) 2 30?).
In this exercise, we want to apply the yirial theorem to the H atom. (a) Does the potential energy for the H atom fulﬁll the conditions for the yirial
theorem to hold? (h) Write down the result of the yirial theorem to the H atom. (c) Check the yirial theorem for the H atom explicitly for the ground state, i.e. the
state with quantum numbers n = 1,1 = 0,111 = 0. You will have to evaluate
the expectation value of the kinetic and potential energy explicitly. Choosing
the right coordinates will simplify the task.