385lec11

385lec11 - PHYS 385 Lecture 11 Bound states of a square well Lecture 11 Bound states of a square well What's important bound states in 1D square

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PHYS 385 Lecture 11 - Bound states of a square well 11 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 11 - Bound states of a square well What's important : bound states in 1D square well minimal conditions for binding examples Text : Gasiorowicz, Chap. 5 Bound states of a square well In the previous lecture, we determined the unbound states of a square well potential in one dimension. E = 0 - V o 2 a By unbound , we mean that E > 0, so the object can escape to infinity. But there may also be bound states (where E < 0), although their existence depends on the nature of the well: the width and depth of the well must satisfy a constraint in order for bound states to exist. In addition, there are a finite number of bound states for a finite well (unlike the Coulomb potential, as we saw in the Bohr model for hydrogen-like atoms). As before, the candidate wavefunctions are exp( iqx ) because V ( x ) is locally constant except at the boundaries | x | = a . Outside of the boundaries, | x | > a , the wavefunctions are still exponentials, but the combination 2 mE / h 2 is complex because E < 0. Thus, the function exp( ikx ) is pure real for pure imaginary k , and may grow or decay with

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This note was uploaded on 09/07/2009 for the course PHYS 385 taught by Professor Davidboal during the Spring '09 term at Simon Fraser.

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385lec11 - PHYS 385 Lecture 11 Bound states of a square well Lecture 11 Bound states of a square well What's important bound states in 1D square

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