(84) Particle in Finite Square Potential Well

This gives where is a positive integer or 1194 these

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Unformatted text preview: the even- infinite- depth potential well solutions specified by Equation (1147). Probably the most surprising aspect of the bound states that we have just described is the possibility of finding the particle outside the well: that is, in the region where . This follows from Equation (1184) and (1185) because the ratio is not necessarily zero. Such behavior is strictly forbidden in classical mechanics, according to which a particle of energy is restricted to regions of space where (Fitzpatrick 2012). In fact, in the case of the ground state (i.e., the lowest energy symmetric state) it is possible to demonstrate that the probability of a measurement finding the particle outside the well is (see Exercise 13) (1195) for a shallow well (i.e., ), and (1196) for a deep well (i.e., ). It follows that the particle is very likely to be found outside a shallow well, and there is a small, but finite, probability of it being found outside a deep well. In fact, the probability of finding the particle outside the well only goes to zero in the case of an infinitely deep well (i.e., )....
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This note was uploaded on 08/25/2013 for the course PHY 315 taught by Professor Staff during the Fall '08 term at University of Texas.

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