Mathematics
Scientific paper
May 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrvd..11.2770b&link_type=abstract
Physical Review D - Particles and Fields, 3rd Series, vol. 11, May 15, 1975, p. 2770-2780.
Mathematics
50
Astronomical Models, Cosmology, Quantum Theory, Gravitons, Orthonormal Functions, Quantum Mechanics, Singularity (Mathematics), Wave Functions
Scientific paper
The quantized Gowdy T-cubed universe is examined from the point of view of a scattering process in superspace. A complete closed set of orthonormal wave functions, which are valid at all times, is obtained for each mode of this model, and a wave function is derived which reduces to a certain initial state near the classical singularity. The exact description of this initial state yields a model with the size and shape parameter of a universe which satisfies an initial free-particle-like equation and is later captured in the N-quamtum state of a rising harmonic-oscillator potential. The expected number of quanta in each mode at times far removed from the singularity is obtained and found to depend only on the constants characterizing the initial state. All expectation values are shown to agree with those obtained by semiclassical and classical methods, except for a smearing out of the basic classical picture by quantum fluctuations.
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