We select for the general Equation "Schrodinger equation":giving the full explicit partial differential equation:

- $x=x$, the linear cartesian coordinate in the x direction
- $H^=−2mℏ_{2} ∂x_{2}∂_{2} +V(x,t)$, which analogous to the sum of kinetic and potential energy in classical mechanics

$iℏ∂t∂ψ(x,t) =[−2mℏ_{2} ∂x_{2}∂_{2} +V(x,t)]ψ(x,t)$

The corresponding time-independent Schrödinger equation for this equation is:

$[−2mℏ_{2} ∂x_{2}∂_{2} +V(x)]ψ(x)=Eψ(x)$