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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
We can't find a solution for E less than 0 (no solution for v).
For energy less then V0 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 V0 particles can move from one side to the
other, but will move slower if they are above the barrier.