In our statistical treatments of quantum systems, we typically neglect any zero-pont energy (i.e. we always assume that the energy of the ground state is zero). Show that the expression for the probability of occupying any given level of a harmonic oscillator is the same whether or not the zero-point energy is included.

In our statistical treatments of quantum systems, we typically neglect any zero-pont energy (i.e. we always assume that the energy of the ground state is zero). Show that the expression for the probability of occupying any given level of a harmonic oscillator is the same whether or not the zero-point energy is included.