# 4.5: Lessons from the square well

- Page ID
- 14770

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The computer demonstration showed the following features:

- If we drop the requirement of normalisability, we have a solution to the time-indepndent Schrödinger Equation at every energy. Only at a few discrete values of the energy do we have normalisable states.
- The energy of the lowest state is always higher than the depth of the well (uncertainty principle).
- Effect of depth and width of well. Making the well deeper gives more eigenfunctions, and decreases the extent of the tail in the classically forbidden region.
- Wave functions are oscillatory in classically allowed, exponentially decaying in classically forbidden region.
- The lowest state has no zeroes, the second one has one, etc. Normally we say that the n th state has n− 1“nodes”.
- Eigenstates (normalisable solutions) for different eigenvalues (energies) are orthogonal.