2.3: Simple Example

We can define all these concepts (velocity, momentum, potential) in one dimensionas well as in three dimensions. Let us look at the example for a barrier

\[V(x)=\left[\left.\begin{array}{cc}
0 & |x|>a \\
V_0 & |x|<a
\end{array} \right\rvert\,\right.\]

We can't find a solution for \(E\) less than 0 (no solution for \(v\) ). For energy less then \(V_0\) the particles can move left or right from the barrier, with constant velocity, but will make a hard bounce at the barrier (sign of \(v\) is not determined from energy). For energies higher than \(V_0\) particles can move from one side to the other, but will move slower if they are above the barrier.

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