Tveter, F.
A Classical Approach to the Schrodinger Equation for a Particle in a Force Field
(10K, LATeX 2e)
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.