Lecture 8- Finite Square Well

Solution for $ψ (x)$

Setting $k^{2} = \frac{2 m}{ℏ ^{2}} (E - V)$

\frac{\partial ^{2} ψ ( x )}{\partial x ^{2}} + k^{2} ψ (x) = 0

General solutions

A sin k x + B sin k x

A e^{ik x} + B e^{- ik x}

Ψ = A e^{i (k x - ω t)} + B e^{- i (k x + ω t)}