A particle moves freely in the two-dimensional region defined by 0 x L and 0

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A particle moves freely in the two-dimensional region defined by 0 ≤ x ≤ L and 0 ≤ y ≤ L.

(a) Find the wave function satisfying Schrödinger’s equation.

(b) Find the corresponding energies.

(c) Find the lowest two states that are degenerate. Give the quantum numbers for this case.

(d) Find the lowest three states that have the same energy. Give the quantum numbers for the three states having the same energy.

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