調和振動子の波動関数（グラフ）

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