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Chinese Physics Letters

Angular Momentum Conserved Coherent State for an Electron in a Uniform Magnetic Field

Hong-Yi Fan, Hui Zou, Yue Fan

Published Oct 1, 1999• 5 citations
Publisher

Abstract

For an electron in the uniform magnetic field, we construct the angular momentum conserved coherent state || r 2 , l ⟩, based on which we establish a new complete and orthonormal ⟨⟨ l,r | representation, where l represents the angular momentum and r the electron's orbit radius. Squeezing of the state | l,r ⟩⟩ is examined.
DOI
10.1088/0256-307x/16/10/002

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Based on the newly constructed state | l , r ⟩⟩ [Fan et al. , Chin. Phys. Lett. 16(1999)706], where l is the angular momentum quantum number and r denotes the electron's orbit radius in a uniform magnetic field, we propose a new angular momentum-phase coherent state by introducing a new operator A . A and A † are annihilation and creation operators in the | l , r ⟩⟩ space, respectively. The coherent state is A 's eigenket and possesses non-orthonormal and overcomplete properties. It is constructed on the certain superposition of zero-angular momentum states along the radius direction.
We show that the newly found complete and orthonormal representation , which is constructed in terms of guiding centers and canonical momenta of an electron moving in a uniform magnetic field, also helps us to establish a systematic phase operator theory. The unitary phase operator, interpreted as a quantity canonically conjugated to the electron angular momentum, manifestly exhibits in the representation its phase behavior. As a byproduct, the phase distribution function, in the correct sense of probability in quantum mechanics, can also be defined by the representation.