== Additional Equation Needed? == 

 The discussion I'm following regarding degenerate matter and degeneracy pressure is the question of when the core of a large star converts to a neutron star, or a black hole.  The usual description is that 'if the pressure exceeds the degeneracy pressure, then the core collapses.'  However, the equation here for degeneracy pressure is not a limit, but appears to be a continuous function of pressure as a function of density. 

 We have one equation that gives the pressure as a function of density, and an inequality that shows that the product of uncertainty in momentum and position has a minimum value.  What's missing is a relationship between (P,rho) and (p,x).  I think with such a conversion, there may be enough information here to turn the Heisenberg inequality into a statement about the maximum density of electrons, and/or the maximum pressure the electron cloud could withstand.