Consider the quantum mechanical problem of a particle trapped in an infinite potential well. The solution to this problem using Schrodinger's equation gives us discrete energy eigenfunctions and eigenvalues. Suppose we already have a particle in some eigenstate, then its energy can be increased only if we impart an amount of energy equal to the difference between its present eigenstate and some other eigenstate (this is similar to an electrom in an atom).
The problem is how can this model be realised. I mean, if we already have the potential well and some particle with an energy not equal to some eigenvalue, then if try to trap this particle, will it instantaneously release energy? Is this a general feature of other quantum mechanical systems? I know that this problem is very ideal but I feel like some essential features like this can be better understood from this problem.