Dynamics of a moving quantum charged particle

Yong-Yi Huang

A classical charged particle moves along a straight line and interacts with a silver atom in its ground state fixed at the origin of coordinates through Biot-Savart coupling. If the silver atom initially lies in a spin superposition state of valence electron, in the co-moving reference frame the projected measurements of the spin of silver’s valence electron along the z direction determine the moving direction of the charged particle. The projected measurements of that spin along the x or the y direction yield straight line motion versions of Schrödinger’s cat state for the charged particle. When the spin coherence state of the silver atom suffers from its environment decoherence, as long as the silver atom’s spin is entangled with the trajectories of the moving charged particle, the measurements on the silver atom’s spin also yield the partial superpositions of different trajectories of the moving charged particle. It is possible to control mechanical motion up to quantum level by the means of quantum measurements.

Elisheva Elbaz

Meng Xiang-Guo, Ji‐Suo Wang, Liang Bao-Long

This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.

Manoj K. Harbola

Application of the Bohr–Wilson–Sommerfeld quantization condition to a charged particle in a uniform magnetic field requires knowledge of the canonical momentum of such a particle, which in turn requires students to know about the vector potential. The canonical momentum in this situation is conventionally obtained by introducing an appropriate additional term involving the corresponding vector potential in the Lagrangian. In this work, we take a different approach to this problem by analyzing it with Maupertuis's principle of least action. We show that satisfying this principle for a charged particle moving in a uniform magnetic field requires that a term proportional to the flux passing through the area enclosed by the particle's trajectory be included in its action. This additional term accomplishes two tasks. First, it facilitates applying the Bohr–Wilson–Sommerfeld quantum condition for a charged particle moving in a uniform magnetic field without using the Lagrangian approach, and, second, it gives the appropriate canonical momentum and Lagrangian for a charged particle in a general electromagnetic field in a straightforward manner.

Fumika Suzuki