Hi...I've come across this question on a past exam, and I can't seem to resolve it!(adsbygoogle = window.adsbygoogle || []).push({});

A particle is incident on a step potential at x=0. The total energy of the particle E, is less then the height of the step, U. The particle has wavefunctions

[tex]$\begin{array}{l}

\psi (x) = \frac{1}{2}\{ (1 + i)e^{ikx} + (1 - i)e^{ - ikx} \} ,x \ge 0 \\

\psi (x) = e^{ - kx} ,x < 0 \\

\end{array}$

[/tex]

Note that k is the same on both sides of the step

a) ….

b.) How must k be related to E and U on both sides of the step and determine the ration E/U

Well on the left, it is just a free wave-function where k=[tex]$k = \frac{{\sqrt {2mE} }}{\hbar }$

[/tex]

On the right k= [tex]$k = i\kappa = \frac{{i\sqrt {2m(U - E)} }}{\hbar }$

[/tex]

Since the k’s are equal this immediately implies that U=0, does it not? In which case the ratio E/U is infinite…

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# A Step potential question

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