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The one dimensional case can be extended easily to the three dimensional case; one might not be satisfied
with such a solution. We will also demonstrate the solution in spherical coordinates. With a harmonic oscillator
potential, Schrödinger's equation in one dimension becomes,
![$\displaystyle -\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2}m\omega^2 x^...
...= \frac{2E}{\hbar \omega} \rightarrow \ \frac{d^2\psi}{d\eta^2}=(\eta^2 -K)\psi$](img37.png) |
(2.1) |
A solution to this equation can be found with the traditional approach.
Subsections
Timothy D. Jones
2007-01-29