Square barrier

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

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

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

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

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern