![]() This is the form best suited for the study of the hydrogen atom. the wave system theory is developed and a general force equation is obtained which is essential to understanding the Schrodinger equation. ![]() For a three-dimensional problem, the Laplacian in spherical polar coordinates is used to express the Schrodinger equation in the condensed form The derivation of the Schrodinger equation will be based on the Lorentz invariance of the wave system. 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. The Schrodinger equation can then be written:įor systems with a spherically symmetric potential, like the hydrogen atom, it is advantageous to use spherical coordinates. ![]() This can be written in a more compact form by making use of the Laplacian operator ![]() In three dimensions, the time-independent Schrodinger equation takes the formįor cartesian coordinates. Schrodinger equation in three dimensions 3-D Schrodinger Equation ![]()
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