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The computer demonstration showed the following features:
- 1.
- If we drop the requirement of normalisability, we have a solution
to the TISE at every energy. Only at a few discrete values of the energy
do we have normalisable states.
- 2.
- The energy of the lowest state is always higher than the
depth of the well (uncertainty principle).
- 3.
- Effect of depth and width of well.
Making the well deeper gives more eigen functions, and decreases
the extent of the tail in the classically forbidden region.
- 4.
- Wave functions are oscillatory in classically allowed, exponentially
decaying in classically forbidden region.
- 5.
- The lowest state has no zeroes, the second one has one, etc. Normally
we say that the nth state has n - 1 ``nodes''.
- 6.
- Eigen states (normalisable solutions) for different eigen values (energies)
are orthogonal.