# Quantum mechanics - potential step problem

I've done potential steps where V > E0 and V < E0, but not where it's equal to 0. How would I go about answering this question? Any help is appreciated.

See below.

• Hi Christopher Ambarchian, and welcome to Physics Stack Exchange! We prefer to have quoted text posted as images so it can be indexed by search engines and is accessible to screen readers. Could you please type out the text from your image? For formulas, use MathJax. – David Z May 21 '20 at 18:51

• If $$V_0=0$$ then it simply means that you're talking about a free particle and the solutions to the free particle TISE are trivially given by the eigenstates of the momentum operator with each eigenvalue of energy being two-fold degenerate (check this!).
• However, you can exploit the fact that $$E\geq 0$$ and treat the case of $$V=0$$ as the limiting case of the $$V\leq E$$ class of cases (you should be able to justify that the procedure for $$V can also handle $$V\leq E$$). Since you have already solved this class of cases, you should be able to simply read off the case of $$V=0$$. Verify that this matches with the results obtained using the first bullet point.