Squeezed States of a Particle in Magnetic Field

Abstract

For a charged particle in a homogeneous magnetic field, we construct stationary squeezed states which are eigenfunctions of the Hamiltonian and the non-Hermitian operator ${\hat{X}}_{\Phi }=\hat{X}\cos \Phi +\hat{Y}\sin \Phi$, $\hat{X}$ and $\hat{Y}$ being the coordinates of the Larmor circle center and $\Phi$ is a complex parameter. In the family of the squeezed states, the quantum uncertainty in the Larmor circle position is minimal. The wave functions of the squeezed states in the coordinate representation are found and their properties are discussed. Also, for arbitrary gauge of the vector potential we derive the symmetry operators of translations and rotations.

RevTex, 12 pages, 4 Postscript figures, submitted to Physics of the Solid State; added references

References in corpus (1)

• Orthogonal localized wave functions of an electron in a magnetic field

Cited by in corpus (2)

• Charged hydrogenic problem in a magnetic field: Non-commutative translations, unitary transformations, and coherent states
• Tomographic Probability Representation for States of Charge moving in Varying Field