Abstract
We have solved the two-dimensional time-dependent Schrödinger equation for a single particle in the presence of a non-uniform magnetic field for initial speed of 10-100 m/s, mass of the particle at 1-10 mp,where mp is the mass of a proton. Magnetic field at the origin of 5-10 T, charge of 1-4 e, where e is the charge of the particle and gradient scale length of 2.610 × 10−5 - 5.219 m. It w as numerically found that the variance, or the uncertainty, in position can be expressed as dσ2r /dt = 4.1ħv0/qB0LB, where m is the mass of the particle, q is the charge, v0 is the initial speed of the corresponding classical particle, B0 is the magnetic field at the origin and LB is the gradient scale length of the magnetic field. In this expression, we found out that mass, m does not affect our newly developed expression.
