Quantum mechanical expansion of a magnetized particle in the presence of a field particle for magnetic fusion plasmas

Abstract

Abstract. The two-dimensional time-dependent Schrödinger equation, for a magnetized proton in the presence of a fixed field particle and of a uniform magnetic field is numerically solved. In the relatively high-speed case, the fast-speed proton has the similar behaviors to those of classical ones. However, in the extension of time, the relatively high-speed case shows similar behavior to the low-speed case: the cyclotron radii both in mechanical momentum and position are appreciably decreasing with time. However, the kinetic energy and the potential energy do not show appreciable changes. This is because of the increasing variances, i.e. uncertainty, both in momentum and position. The increment in variance of momentum corresponds to the decrement in the magnitude of mechanical momentum in a classical sense: Part of energy is transferred from the directional (classical kinetic) energy to the uncertainty (quantum mechanical zero-point) energy.