Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition

Broadbridge, Philip; Deutscher, K

doi:10.26181/5fffd7f344e5a

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Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition

journal contribution

posted on 2021-01-14, 05:34 authored by Philip BroadbridgePhilip Broadbridge, K Deutscher

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. For a scalar field in an exponentially expanding universe, constituent modes of elementary excitation become unstable consecutively at shorter wavelength. After canonical quantization, a Bogoliubov transformation reduces the minimally coupled scalar field to independent 1D modes of two inequivalent types, leading eventually to a cosmological partitioning of energy. Due to accelerated expansion of the coupled space-time, each underlying mode transits from an attractive oscillator with discrete energy spectrum to a repulsive unit with continuous unbounded energy spectrum. The underlying non-autonomous Schrodinger equation is solved here as the wave function evolves through the attraction-repulsion transition and ceases to oscillate.

Funding

The second author gratefully acknowledges support of the Australian Research Council for project DP160101366.

History

Publication Date

2020-01-01

Journal

Symmetry

Volume

12

Issue

6

Article Number

943

Pagination

24p. (p. 1-24)

Publisher

MDPI

ISSN

2073-8994

Rights Statement

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