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

Journal Article · Sat Sep 15 04:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.2049· OSTI ID:6056668

Homma, T; Inamoto, T; Miyazaki, T ^[1]

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1. Department of Physics, Science University of Tokyo, Kagurazaka 1-3, Shinjuku-ku, Tokyo 162 (Japan)

Dirac-bracket quantization of the nonrelativistic particle whose motion is constrained on the hypersurface {ital f}({ital 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 {ital df}({ital x})/{ital 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 Schroedinger equation in the former system.

• OSTI ID: 6056668
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:6; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
HAMILTONIANS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE KINEMATICS
PHASE SPACE
QUANTIZATION
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
SPACE
WAVE EQUATIONS