# Wave function of harmonic oscillator (chart) Calculator

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

Wave function of harmonic oscillator (chart)
 [1-4] /4 Disp-Num5103050100200
[1]  2018/11/11 09:01   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
Wave functions and energy values. The plots are cool too.
[2]  2017/10/01 02:22   Male / 40 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Create wavefunction illustration of vibrational mode harmonic (chemistry)
Comment/Request
NICE program!
[3]  2013/03/17 14:49   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
to incorporate in the topic on Oscillator
[4]  2010/04/11 16:01   Male / 40 level / A teacher / Very /
Comment/Request
It gives the details of the motion

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