So I have this question that goes like this, for a classical 1D system we are given an Hamiltonian of the form of an Harmonic Oscilator. However the term for the potential is infite when ##x\leq0## and the usual harmonical oscillator potential otherwise. The question is: is the equipartition theorem valid for each term of the Hamiltonian? Attempt at a solution Now for all I've read the only condition on the equipartition theorem is that the system must be in thermal equilibrium, so I see no reason for it not to be valid, although I don't know how to properly justify this. However, I have a gut feeling that the infinite potential will make the theorem invalid, but once again I have no idea how to justify this.