Studies of the Schroedinger-Newton Equations in D Dimensions

Simple item page
dc.creatorMelko, R. G.
dc.creatorMann, R. B.
dc.date2000-11-01
dc.date.accessioned2026-07-07T03:25:22Z
dc.date.available2026-07-07T03:25:22Z
dc.descriptionWe investigate a $D$ dimensional generalization of the Schroedinger-Newton equations, which purport to describe quantum state reduction as resulting from gravitational effects. For a single particle, the system is a combination of the Schroedinger and Poisson equations modified so that the probability density of the wavefunction is the source of the potential in the Schroedinger equation. For spherically symmetric wavefunctions, a discrete set of energy eigenvalue solutions emerges for dimensions $D<6$, accumulating at D=6. Invoking Heisenberg's uncertainty principle to assign timescales of collapse correspoding to each energy eigenvalue, we find that these timescales may vary by many orders of magnitude depending on dimension. For example, the time taken for the wavefunction of a free neutron in a spherically symmetric state to collapse is many orders of magnitude longer than the age of the universe, whereas for one confined to a box of picometer-sized cross-sectional dimensions the collapse time is about two weeks.
dc.descriptionLatex, 18 pages, 11 figures
dc.identifierhttps://arxiv.org/abs/gr-qc/0011004
dc.identifierhttp://arxiv.org/abs/gr-qc/0011004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/33680
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleStudies of the Schroedinger-Newton Equations in D Dimensions
dc.typetext

Files

Collections

arXiv