Wave Function

#Physics
Solves the Schrodinger equation

Topics

• Spherical Wave Function

$\displaystyle [\Psi(\vec{r},t)]=\frac{1}{\sqrt{ L^{n} }}$

• Units for wave function in $\displaystyle n$ dimensions
• $\displaystyle L$ is in units of length

$\displaystyle \int_{-\infty}^{\infty} \lvert \Psi\rvert^{2} , \mathrm{d}\vec{r}=1$

• Obeys Normalization

$\displaystyle f(x)=\sum_{n = 1}^{\infty}c_{n}\psi_{n}(x)$

• $\displaystyle c_{n}$ is a Wave Function Weighting Coefficient

$\displaystyle {\left\langle{\psi_{n},\psi_{m}}\right\rangle}=\int {\mathbb{R}}\psi^{*}{n}\psi_{m} , \mathrm{d}x=\delta_{nm}$

• Stationary states orthogonality condition