![]() The condition for normalization is then The sin terms drop out, leavingįor the finite potential well, the solution to the Schrodinger equation gives a wavefunction with an exponentially decaying penetration into the classicallly forbidden region.Ĭonfining a particle to a smaller space requires a larger confinement energy. This constrains the form of the solution to which requiresĪnd after normalization, the wavefunction isįor the particle in a box with infinite walls, the probability must be equal to one for finding it within the box. For a particle inside the box a free particle wavefunction is appropriate, but since the probability of finding the particle outside the box is zero, the wavefunction must go to zero at the walls. ![]() ![]() Assume the potential U(x) in the time-independent Schrodinger equation to be zero inside a one-dimensional box of length L and infinite outside the box.
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