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A particle of mass m is in an infinite square well of width L.

Show that the solution to the time-independent Schrodinger equation (H%u03C8 = E%u03C8) is of the form %u03C8(x) = Asinkx+Bcoskx for 0 < x < L, and 0, otherwise. Use boundary conditions to simplify the form of the equation, find k, and a consequence, determine the allowed energies for the system.

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