A Treatise of Human Nature taste to be in the other), arguing that unextended perceptions must somehow exist without having a location. But the contrary problem arises for dualists: how can extended perceptions (of extended objects) possibly be conjoined to a simple substance? Indeed, Hume waggishly adds, this is basically the same problem that theologians commonly press against Spinoza's naturalistic metaphysics: thus if the theologians manage to solve the problem of extended perceptions belonging to a simple substance, then they give "that famous atheist" Spinoza a solution to the problem of extended objects as modes of a simple substance. Finally, Hume examines "causal relations", arguing
A priori probability case of the hydrogen atom or Coulomb potential (where the evaluation of the phase space volume for constant energy is more complicated) one knows that the quantum mechanical degeneracy is formula_56 with formula_57. Thus in this case formula_58. In statistical mechanics (see any book) one derives the so-called distribution functions formula_59 for various statistics. In the case of Fermi-Dirac statistics and Bose-Einstein statistics these functions are respectively These functions are derived for (1) a system in dynamic equilibrium (i.e. under steady, uniform conditions) with (2) total (and huge) number of particles formula_61 (this condition determines the constant formula_62), and (3)