Nonlinear Phenomena in Complex Systems, 2014, Vol.17, No.4, pp.358-363

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2014, Vol.17, No.4, pp.358-363

A Solution of the Discrete Wheeler–Dewitt Equation in the Vicinity of Small Scale Factors and Quantum Mechanics in the Space of Negative Constant Curvature
S. L. Cherkas and V. L. Kalashnikov

The asymptotic of the solution of the discrete Wheeler–DeWitt equation is found in the vicinity of small scale factors. It is shown that the problem is equivalent to the solution of the stationary Schrödinger equation in the (super) space of negative constant curvature. The minimum positive eigenvalue is found from which a continuous spectrum begins.

Key words: Wheeler–DeWitt equation, superspace, spaces of negative constant curvature, quantum mechanics in curved space

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