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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 ) and ( 6.20 ), subtract eqs. ( 6.19 ) from ( 6.21 ), subtract ( 6.20 ) from ( 6.18 ), and add ( 6.19 ) and ( 6.21 ). We find
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern