Geometrization of the Schrödinger equation: Application of the Maupertuis Principle to quantum mechanics

Antonia Karamatskou, Hagen Kleinert
2014 International Journal of Geometric Methods in Modern Physics (IJGMMP)  
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 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
more » ... ion we calculate the semiclassical expansion of the particle density.
doi:10.1142/s0219887814500662 fatcat:cwypbe54jjhczlh6kxrpwc4fuy