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Abstract:
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ABSTRACT
The Schrödinger equation is solved for a harmonic oscillator whose potential is moving classically with an arbitrary time-dependent acceleration. Complete solutions are obtained, and several probability distributions are studied with particular emphasis on the classical motion of the entire wave packet. The probability distribution in the lab frame conserves its original shape as it would normally have in the case of the stationary potential, but moves classically as a whole according to the trajectory that is determined by the time dependent acceleration. A quantum paradox emerging from these solutions is introduced by letting the system start its classical motion in the ground state, and later observing positive probabilities for the system to be in excited states.
FOREWORD
This paper will mainly focus on analytically solving the Schrödinger equation with an explicitly time dependent potential. The problem of solving the Schrödinger equation with time dependent potential has interested many physicists over the past few decades due to its applications to diverse physical systems. Although, numerical methods are also widely used to solve these equations, the complete analytical solution is more valuable as it enables us to gain important information about the system that would otherwise be lost if numerical methods were applied. |
