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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.
 Fall '08
 Staff
 Mass, Waves And Optics

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