Affiliations: [a] Graduate School of Engineering, Hokkaido University, Sapporo, Japan | [b] Faculty of Engineering, Hokkaido University, Sapporo, Japan
Correspondence:
[*]
Corresponding author: P.K. Chan, Graduate School of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan. E-mail:chan@fusion.qe.eng.hokudai.ac.jp
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.
Keywords: Uncertainty, field particle, uniform magnetic field, quantum mechanical expansion, anomalous diffusion
