Schrödinger Wave Equation

1D

$$i\hslash {\Psi }_t=-\frac{{\hslash }^2}{2m}{\Psi }_{xx}\text{where }\Psi =\Psi (x,t)$$

3D Time-dependent Equation

$$-\frac{{\hslash }^2}{2m}\left({\Psi }_{xx}+{\Psi }_{yy}+{\Psi }_{zz}\right)+V\Psi =i\hslash {\Psi }_t\text{where }\Psi =\Psi (x,y,z,t)$$

3D Time-independent Equation

$$-\frac{{\hslash }^2}{2m}\left({\psi }_{xx}+{\psi }_{yy}+{\psi }_{zz}\right)+V\psi =E\psi \text{where }\psi =\psi (x,y,z)$$

Schrödinger Wave Equation for Hydrogen Atom

See also

Wave Quantum Mechanics