Schrödinger equation for the nonrelativistic particle constrained on a hypersurface in a curved space

Details Schrödinger equation for the nonrelativistic particle constrained on a hypersurface in a curved space Schrödinger equation for the nonrelativistic particle constrained on a hypersurface in a curved space

Sep 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phrvd..42.2049h&link_type=abstract

Physical Review D (Particles and Fields), Volume 42, Issue 6, 15 September 1990, pp.2049-2056

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18

Quantum Mechanics, Other Topics In General Relativity And Gravitation

Scientific paper

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.

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