# Wave function of harmonic oscillator (chart)

## Calculates a table of the quantum-mechanical wave function of one-dimensional harmonic oscillator and draws the chart.

 It calculates values of the position x in the unit of α=√(2πmω/h)=1.
Quantum number n
 n=0,1,2,3,...
[ Initial position x
 of electron
Increment
 , Repetition ]

 $\normal The\ wave\ function\ \psi(x)\\\hspace{15}of\ the\ quantum\ harmonic\ oscillator\\[10pt](1)\ [-{\large\frac{\hbar^2}{2m}}{\large\frac{d^2}{dx^2}}\psi+{\large\frac{1}{2}}m\omega^2x]\psi=E\psi\\\hspace{170} E=\hbar\omega(n+{\large\frac{1}{2}})\\\vspace{10}(2)\ \psi_{n}(x)=\sqrt{\large\frac{\alpha}{2^nn!\sqrt{\normal\pi}}}H_n(\alpha x)e^{\small -\frac{1}{2}(\alpha x)^2}\\\hspace{170}\alpha=\sqrt{\large\frac{m\omega}{\hbar}}\\\hspace{20}{\large\int_{\small-\infty}^{\qquad\qquad\quad\small\infty}}\psi_{n}(x)\psi_{n'}^*(x)dx=\delta_{nn'}\\$

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