The Schrodinger Equation, Internal Temperature and Fisher Information

 In this note, we consider the time-independent Schrodinger equation written in terms of Fisher information density and internal temperature. We note, that for the ground state oscillator case, Fisher information density becomes proportional to entropy density and internal temperature becomes a constant. This leads to an equation which is consistent with the maximization of entropy (for this special case) and leads to classical statistical mechanical results. If one tries to generalize to potentials other than the oscillator, one obtains a theory completely different from quantum mechanics, namely classical statistical mechanics. (For the oscillator potential, however, the two have the same form.) Finally, we note that the form of temperature as a function of x, obtained from Boltzmann transport considerations equals the extremization of Fisher information density.