Title:
Geometrization of the Schrödinger equation
Subtitle:
Application of the Maupertuis Principle to quantum mechanics
Author(s):
Karamatskou, Antonia; Kleinert, Hagen
Year of publication:
2014
Available Date:
2015-02-11T10:46:54.133Z
Abstract:
In its geometric form, the Maupertuis Principle states that the movement of a
classical particle in an external potential V(x) can be understood as a free
movement in a curved space with the metric gμν(x) = 2M[V(x) - E]δμν. We extend
this principle to the quantum regime by showing that the wavefunction of the
particle is governed by a Schrödinger equation of a free particle moving
through curved space. The kinetic operator is the Weyl-invariant
Laplace–Beltrami operator. On the basis of this observation, we calculate the
semiclassical expansion of the particle density.
Part of Identifier:
ISSN (print): 0219-8878
Keywords:
Schrödinger equation in curved space
quantum particle motion in curved space
exact solutions
curved space quantum mechanics
geometric physics
DDC-Classification:
530 Physik
Publication Type:
Wissenschaftlicher Artikel
Also published in:
International Journal of Geometric Methods in Modern Physics. - (2014), 11,
Artikel Nr. 1450066
URL of the Original Publication:
DOI of the Original Publication:
Department/institution:
Physik
Institut für Theoretische Physik