## Per K. Jakobsen and Valentin V. Lychagin

# Maximum Entropy Wave functions

## (*Lobachevskii Journal of Mathematics, Vol.23, pp.29-56* )

In this paper we use the classical Maximum Entropy principle to define maximum
entropy wave functions. These are wave functions that maximize the entropy
among all wave functions satisfying a finite set of constraints in the form of
expectation values.This lead to a nonlinear equation for the wave function
that reduce to the usual stationary Schrödinger equation if the energy is
the only constraint and the value of the constraint is an eigenvalue. We
discuss the extension of the thermodynamical formalism to this case and apply
our general formalism to several simple quantum systems, the two-level
atom,the particle in a box, the free particle and the Harmonic Oscillator and
compare with the results obtained by applying the usual von Neumann quantum
statistical method to the same systems.

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