Motion of a Nonrelativistic Quantum Particle in Non-commutative Phase Space

S. Chaturvedi, R. Jagannathan, V. Srinivasan +1 more

Fateme Hoseini, Kai Ma, Hassanabadi Hassan

The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.

Luigi Accardi

Takahiro Homma, Tadashi Inamoto, Tadashi Miyazaki

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 Schr\"odinger equation in the former system.

Philip C. Tillman, George A. J. Sparling

In this paper we construct the commutators of the Fedosov * (a generalization of the Moyal star product) on the phase space of S2. It is shown that this product obeys the standard angular momentum commutation relations in ordinary nonrelativistic quantum mechanics. The purpose of this paper is three-fold. One is to find an exact, non-perturbative solution to the commutators of the Fedosov *. The other is to verify that these commutation relations correspond to angular momentum commutation relations as in ordinary nonrelativistic quantum mechanics. The last is to show a more general computation of the Fedosov *; essentially undeforming Fedosov's algorithm.

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