3-D Schrodinger Equation

In three dimensions, the time-independent
Schrodinger equation takes the form

for cartesian coordinates. This can be written in a more compact form
by making use of the Laplacian
operator

The Schrodinger equation can then be written:

For systems with a spherically symmetric potential, like the hydrogen
atom, it is advantageous to use spherical
coordinates.

Index

Schrodinger
equation concepts

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Quantum Physics

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Schrodinger Equation, Spherical Coordinates
If the
potential of the physical system to be examined is spherically symmetric,
then the Schrodinger equation in spherical
polar coordinates can be used to advantage. For a three-dimensional
problem, the Laplacian
in spherical polar coordinates is used to express the Schrodinger equation
in the condensed form

Expanded,
it takes the form

This
is the form best suited for the study of the hydrogen
atom.

Index

Schrodinger
equation concepts

HyperPhysics*****
Quantum Physics

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