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In the scenario of a particle in an infinite potential well, there are discrete energy levels, i.e.##E=\hbar ^2 n^2 \pi ^2/ (2 m L^2)## where L is the width of the potential well, and n takes on positive integers. But what will happen if I put a particle of energy ##E_i## that is not a multiple of ##E=\hbar ^2 \pi ^2/ (2 m L^2)## into the potential well? I am thinking that the answer may be that there is some uncertainty in the ##E_i## so the particle can always takes on an energy level in the potential well within this allowable range of energy. Is this correct? What exactly is will happen in this case? Thank you!

Best,

Alan