1.I .9 F. 9 \mathrm{~F} \quad

Quantum Mechanics | Part IB, 2001

A quantum mechanical particle of mass mm and energy EE encounters a potential step,

V(x)={0,x<0V0,x0V(x)= \begin{cases}0, & x<0 \\ V_{0}, & x \geqslant 0\end{cases}

Calculate the probability PP that the particle is reflected in the case E>V0E>V_{0}.

If V0V_{0} is positive, what is the limiting value of PP when EE tends to V0V_{0} ? If V0V_{0} is negative, what is the limiting value of PP as V0V_{0} tends to -\infty for fixed EE ?

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