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Please try to include the following
Steps to the Analytic Method:
1) Dimensionless Form of DE
<math>let \xi = \sqr [(m\omegax}/\hbar)] </math> and <math> K=(2E)/(\hbar\omega). </math>
Then we can use the dimensionless form of the Schrodinger <math> \frac{\partial^2}{\partial x^2}=(\xi^2-K)\psi(x) </math>
<math> \hat{H}=\frac{p^2}{2m}+V(x)=-\frac{\hbar^2}</math>
{2m}\frac{\partial^2}{\partial x^2}+\frac{1}{2} k \strike{\omega} x^2. </math>
2)
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