Abstract:

For a free particle in finite container，in some thermodynamic statistics textbooks，the density of energy states is deduced based on momentum discrete values due to de Broglie relations and standing wave conditions from semi-classical quantum images. However，according to quantum theory，the particle in infinite potential well has energy eigenstates rather than momentum eigenstates. In this paper，we derive the state density of free particles in finite volume based on its energy eigenstates，and the results are in agreement with textbook. But our treatment seems to be more nature.

Key words: density of states, infinite potential well, energy eigenstate