SCHRODINGER EQUATION FOR THE NONRELATIVISTIC PARTICLE CONSTRAINED ON A HYPERSURFACE
1993 年 87 巻 1 号 p. 1-33
詳細
1993 年 87 巻 1 号 p. 1-33
Dirac-bracket quantization of the nonrelativistic particle whose motion is constrained on the hypersurface f(x) = constant embedded in a general curved space is discussed. The noncanonical nature of commutation relations makes it difficult to obtain the coordinate representation of momentum operators. Hence the system with the derivative-type constraint df(x)/dt = 0 is alternatively quantized by treating carefully the operator-ordering problem. In this system it is shown that no constraints exist on coordinates and momenta and that one can thus have a coordinate representation, which leads, in turn, to the representation and the Schrodinger equation in the system with constraint f(x) = constant.
