The Expectation Value of in the Ground State

For , there is no angular dependence to the wavefunction so no velocity except in the radial direction. So it makes sense to compute the radial component of the velocity which is the full velocity.

We can find the term for in the radial equation.

Since
, we get

For , the RMS velocity is or

We can compute the expected value of the kinetic energy.

This is what we expect from the Virial theorem.

Jim Branson 2013-04-22