Solving the Time-Independent Schrödinger Equation for a Step Potential

[captainjack2000]

Considering a step potential of V(x) = o when x<o and V(x) = Vo when x>o so step occurring at origin of x axis.
Write down in words the strategy for solving it.

Answer:
Solve the time-independent schrodinger equation for V=o when x<o and find the solution for the free particle wave function at x<o, which describes the general solution of the standing wave.
Solve the Time-independent schrodinger equation for V=Vo when x=o to find the solution for one positive plus one negative exponential decay, where the positive exponential decay does not make physical sense since a solution that gradually goes to zero is expected.
At the boundary x=o so both solutions equal each other. equate then to find solution to continuous wave over the boundary.

Could someone tell me if this is right

thank you

 

[BigJDubs]

Yes, this is an accurate strategy for solving the step potential of V(x) = 0 when x < 0 and V(x) = Vo when x > 0.