(a) Calculate ⟨V⟩ for the ground state of hydrogen. Show that E=⟨V⟩/2. What is ⟨K⟩, the expectation value of the kinetic energy, for the ground state? Show that these expectation values obey the virial theorem from classical mechanics.
(b) Calculate ⟨V⟩ for the ground state of the isotropic three-dimensional harmonic oscillator. How are ⟨K⟩ and ⟨V⟩ related for the oscillator? What do you expect based on the virial theorem? Explain.