- #1
bb1414
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The time-dependent Schrodinger equation is given by:
Obviously, there is a laplacian in the kinetic energy operator. So, I was wondering if the equation was rearranged as
then does there exist a wave function ## \psi## that satisfies Laplace's equation
so that
If so, can the solution then be a set of spherical harmonics, which is commonly found when dealing with Laplace's equation in other areas?
##-\frac{\hslash^{2}}{2m}\triangledown^{2}\psi+V\psi=i\hslash\frac{\partial }{\partial t}\psi##
Obviously, there is a laplacian in the kinetic energy operator. So, I was wondering if the equation was rearranged as
##-\frac{\hslash^{2}}{2m}\triangledown^{2}\psi=i\hslash\frac{\partial }{\partial t}\psi-V\psi##
then does there exist a wave function ## \psi## that satisfies Laplace's equation
##\triangledown^{2}\psi=0##
##\triangledown^{2}\psi=i\hslash\frac{\partial }{\partial t}\psi-V\psi=0##