Quantum revivals in the motion of an electron in a magnetic field

F. Suekane

Thierry Champel

Tsuyoshi Ueta

The time evolution of a Gaussian wave packet of an electron, which is confined in a quantum dot subjected to uniform magnetic fields, is analytically studied in terms of the exact Feynman kernel. The central position of the wave packet follows the classical trajectory. Although the motion of the central position is aperiodic due to its dual period, the variance of the probability density changes periodically. If the shape of the initial wave packet is the same as that of the wave function of the ground state, its shape never alters. For more general systems in which the periodic full revival of electron wave packets is realized, the characteristic of energy eigenvalues is discussed.

Earle H. Kennard

G. A. Vugalter, A. K. Das, V. A. Sorokin

This paper deals with a simple quantum system which, in addition to being of general interest, can be discussed in an advanced undergraduate course on quantum mechanics. The system consists of a charged particle on a ring of fixed radius—a rigid charged rotator. For this system we have analytically investigated the influence of a dc magnetic field and the symmetry of an initial wavefunction on the scenario of perfect quantum revivals. Using Gisin’s model, we discuss the decay of revivals in the presence of dissipation. Some of our analytical results have been numerically illustrated for Gaussian coherent states. We have also studied the influence of a δ-potential on quantum revivals in this system.

Katherine Newton, J.D.F. Franklin