Hilbert space for charged particles in perpendicular magnetic fields

梁麦林, 张亚彬, 杨瑞林 +1 more

For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, the Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the motion of the charged particle along the magnetic field has the effect of increasing the magnetic field. In the classical limit, matrix elements of the velocity operator related to the probability give a clear physical picture. Along an effective magnetic field, the mechanical momentum is conserved and the motion perpendicular to the effective magnetic field follows a round orbit. If using the velocity operator defined by the coordinate operators, the motion becomes complicated.

V. V. Dodonov

Marin Drinov Academic Publishing House, Guillermo Capobianco, Walter Reartes

In this paper we develop the quantization of a particle in the plane under the influence of a perpendicular magnetic field using the geometric quantization with half--forms in Hilbert space of holomorphic functions. An original coordinate transformation is applied to convert the problem into a system of harmonic oscillators. Then, it is solved highlighting the relationship between different representations. We emphasize the isomorphism between the holomorphic representation and the Schrödinger representation.

Stephen P. Martin

Yu. G. Pavlenko, Alexander S. Dement'ev

Arnaud Ralko, Trong Tuong Truong

We discuss the occurence and properties of exact singular anyonic wave functions describing stationary states of two identical charged particles moving on a plane and under the influence of a perpendicular uniform magnetic field.