Fall 2006 5 Qm

A particle with mass m and energy E moves in the one-dimensional potential V(x) given by V(x)=0 for x < 0 and V(x)=$-V_0$ for $x \ge 0$ where $V_0 \ge 0$.

(a) Solve the time independent Schödinger equation for the wavefunction $\psi (x)$ at all values of x with the boundary condition that the incident flux is from $x = - \infty$.

(b) Compute the transmission and reflection probabilities from your results in (a).

(c) What are the transmission and reflection probabilities in the limits $V_0 \rightarrow 0$ and $V_0 \rightarrow \infty$?

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Answer

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