06-19 Tveter, F.

A Classical Approach to the Schrodinger Equation for a Particle in a Force Field (10K, LATeX 2e) Jan 23, 06

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Abstract. A common approach to the Schrodinger equation is to start with a well known wave function solution to a specific problem, apply the corresponding Schrodinger equation and show that the result is equivalent to the classical Hamiltonian energy equation. In this paper the starting point is the classical Hamiltonian energy equation for a free particle under influence of a force potential. An appropriate variable transformation is applied, and the equation for the corresponding generator function that solves the problem is identified. The relationship between the wave function and the generator function is found by studying the momentum in the two formalisms. Assumptions necessary to approach the Schrodinger equation are identified. The approach shown here leads to an equation that is close to the Schrodinger equation, differing only by the appearance of a term containing the total time derivative of the probability density.

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