Schrodinger Equation for the Nonrelativistic Particle Constrained on a Hypersurface in a Curved Space
May 28, 1990
27 pages
Published in:
- Phys.Rev.D 42 (1990) 2049-2056
Report number:
- Print-90-0316 (SCIENCE U.)
Citations per year
Abstract: (APS)
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.References(3)
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