# Potential step solution is not normalizable

If you try to integrate the solution of the potential step,

http://en.wikipedia.org/wiki/Solution_of_Schr%C3%B6dinger_equation_for_a_step_potential#Solution

you will notice that it diverges! Doesn't that mean that the solution is physically incorrect?

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In quantum physics there are often "large-size" (also called infrared) divergences. They're not very problematic, since generic real life systems are typically finite slabs of matter, so no solution can extend to infinity. –  Vibert Apr 1 '13 at 10:26