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I am aware how the formula is derived. The main form of the formula is a solution of Schrodinger's equation which books say is not derived from anything more fundalmental.

But is the fact that the energy levels are depedent on L intuitive? If so why? Could you say that a longer well would mean that the energy of the electron is distributed more evenly for each position x in the well? Hence the energy of the electron is lower at each x in the well for a particular state in a longer well?