## Related questions with answers

Question

A finite potential energy function U(x) allows $\psi(x),$ the solution of the time-independent Schrödinger equation, to penetrate the classically forbidden region. Without assuming any particular function for U(x), show that $\psi(x)$ must have an inflection point at any value of x where it enters a classically forbidden region.

Solution

VerifiedStep 1

1 of 3We have the wave function $\psi(x)$ as follows:

$\psi(x) =\left\{\begin{array} {lll} C\exp^{+\alpha x} & x<0 \\ A \sin(kL)+B \cos(kL) & 0 \leq x \leq L \\ G \exp^{-\alpha x } & x > L \end{array} \right.$

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