Quantum Effects of an Extra Compact Dimension on the Wave Function of the Universe
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We extend the direct quantum approach of the standard FRW cosmology from 4D to 5D and obtain a Hamiltonian formulation for a wave-like 5D FRW cosmology. Using a late-time approximation we isolate out a y-part from the full wave function of the 5D Universe. Then we find that the compactness of the fifth dimension y yields a quantized spectrum for the momentum $P_{5}$ along the fifth dimension, and we show that the whole space-part of the wave function of the 5D Universe satisfies a two-dimensional Schrödinger equation.
10 pages, no figures; to appear in Int. J. Theor. Phys. (2002)
10 pages, no figures; to appear in Int. J. Theor. Phys. (2002)