2.3: Simple Example

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Nov 3, 2024
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- 2.2: Energy Function
- 3: The Schrödinger Equation

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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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