# Gibbs sum

1. Nov 16, 2004

### JamesJames

Gibbs sum DILEMNA

Consider a system that maybe unoccupied with energy zero or occupied by one particle in either of two states, one of energy zero and one of
energy $$\epsilon_{0}$$. Allow the possibility that the orbital at 0 and at $$\epsilon_{0}$$ may be each occupied by one particle at the same time. What is the Gibbs sum Z?

The Gibbs sum is given by

Z = $$\sum \lambda^{N}exp(-\epsilon_{S(N)}/\tau)$$

where N is the number of particles in each state.

Here is what I think:

Z = $$\lambda^{1}exp(-\epsilon_{0}/\tau) + \lambda^{1}exp(-\epsilon_{0}/\tau)$$

Reasoning: I think that N = 1 since it MUST BE OCCUPIED. I feel that the energy must always be $$\epsilon_{0}$$ since the orbital may be occupied by one particle at the same time....I am not at all convinced about this explanation and need clarification.

What is meant by "each occupied by one particle at the same time" in terms of its effect on the Gibbs sum?

Last edited: Nov 16, 2004