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Particle in a box function

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Particle in a box

For the particle in a box, is the function Ψ(x)=Cx(L-x) a possible state of the system? (C is constant) Justify answer.
(the parameter l in the wavefunction is the length of the box)

V(x)=∞ V(x)=∞

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The expert examines particles in a box function.