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 \{\array{
0 &|x| > a\cr
{V }_{
0}&|x| < a } \right \}
| (2.5) |
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.