Abstract

The eigenvalue equation of the dynamical Schrödinger operator in polar coordinates without potential is considered. An integral transformation in terms of the Bessel's functions is suggested as a solution. The eigenvalue equation is simplified to an ordinary equation in the time variable. The Schrödinger propagator is calculated with the solution of the eigenvalue equation, and used to find explicitly the wave function of the Wheeler–de Witt equation that describes gravity plus a perfect fluid.

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