Schrödinger equation for a one dimensional particle

$x ∣ = x$ , the linear cartesian coordinate in the x direction
$\hat{H} = - \frac{ℏ ^{2}}{2 m} \frac{\partial ^{2}}{\partial x ^{2}} + V (x, t)$ , which analogous to the sum of kinetic and potential energy in classical mechanics

Equation 12. Schrödinger equation for a one dimensional particle

i ℏ \frac{\partial ψ ( x , t )}{\partial t} = [- \frac{ℏ ^{2}}{2 m} \frac{\partial ^{2}}{\partial x ^{2}} + V (x, t)] ψ (x, t)

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

[- \frac{ℏ}{2 m} \frac{\partial ^{2}}{\partial x} + V (x)] ψ = E ψ (x)

Ancestors