Square barrier - Square barrier A slightly more involved...

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Square barrier A slightly more involved example is the square potential barrier, an inverted square well, see Fig. 6.3 . Figure 6.3: The square barrier. We are interested in the case that the energy is below the barrier height, . If we once again assume an incoming beam of particles from the right, it is clear that the solutions in the three regions are (6.16) Here (6.17) Matching at and gives (use and (6.18) (6.19) (6.20) (6.21) These are four equations with five unknowns. We can thus express for of the unknown quantities in one other. Let us choose that one to be , since that describes the intensity of the incoming beam. We are not interested in and , which describe the wave function in the middle. We
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can combine the equation above so that they either have or on the right hand side, which allows us to eliminate these two variables, leading to two equations with the three interesting unknowns , and . These can then be solved for and in terms of : The way we proceed is to add eqs. ( 6.18
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This note was uploaded on 11/09/2011 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.

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Square barrier - Square barrier A slightly more involved...

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