Numerical Analysis of Schrödinger Equation for a Magnetized Particle in the Presence of a Field Particle

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We have solved the two-dimensional time-dependent Schödinger equation for a magnetized proton in the presence of a fixed field particle with an electric charge of 2×10−5e, where e is the elementary electric charge, and of a uniform megnetic field of B = 10 T. In the relatively high-speed case of v0 = 100 m/s, behaviors are similar to those of classical ones. However, in the low-speed case of v0 = 30 m/s, the magnitudes both in momentum mv = |mv|, where m is the mass and v is the velocity of the particle, and position r = |r| are appreciably decreasing with time. However, the kinetic energy K = m〈v2〉/2 and the potential energy U = 〈qV〉,where q is the electric charge of the particle and V is the scalar potential, 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 momentum: Part of energy is transfered from the directional (the kinetic) energy to the uncertainty (the zero-point) energy.