Schrödinger equation for the nonrelativistic particle constrained on a hypersurface in a curved space
Abstract
Dirac-bracket quantization of the nonrelativistic particle whose motion is constrained on the hypersurface f(x)=const embedded in a general curved space is discussed. The noncanonical nature of commutation relations makes it difficult to obtain the coordinate representation. Then the system with the derivative-type constraint df(x)/dt=0 is alternatively quantized, treating carefully the operator-ordering problem. In this system it is shown that there exist no constraints on coordinates and momenta and that one can thus have a straightforward representation, which leads, in turn, to the representation and the Schrödinger equation in the former system.
- Publication:
-
Physical Review D
- Pub Date:
- September 1990
- DOI:
- 10.1103/PhysRevD.42.2049
- Bibcode:
- 1990PhRvD..42.2049H
- Keywords:
-
- 03.65.-w;
- 04.90.+e;
- Quantum mechanics;
- Other topics in general relativity and gravitation