Statistical mechanics of quantum mechanical particles with hard cores

The definition of the thermodynamic pressure of a quantum mechanical system of hard core particles is considered for a wide variety of boundary conditions and a large class of interactions. It is shown that the pressure can be defined for elastic walls and that in the limit of an infinite system the thermodynamic pressure both exists and is independent of the coefficient of elasticity. Similarly if repulsive wall boundary conditions are used the thermodynamic pressure exists. Unfortunately it has not been possible to demonstrate that the two pressures obtained are identical but a number of their properties and interrelationships are established.