{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter2_23 - P T is defined by P T = 1-P R = 0 Probability...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PHY4604 R. D. Field Department of Physics Chapter2_23.doc University of Florida Infinite Step Potential Time-Independent Schrödinger Equation: Look for solutions of the time-dependent Schrödinger equation of the form h / ) ( ) , ( iEt e x t x = Ψ ψ . Substituting Ψ (x,t) into the time dependent equation yields ) ( )) ( ( ) ( 2 2 2 2 x x V E dx x d m ψ ψ = h . Consider a potential V(x) such that V(x)=0 for x < 0 and V(x) = for x 0 . Left Region (x < 0): In this region ) ( ) ( 2 2 2 x k dx x d L L ψ ψ = with 2 2 h mE k = and the most general solution is ikx L ikx L L e B e A x + = Φ ) ( Right Region (x 0): In this region ψ R (x) = 0 . Boundary Conditions: In this case ψ L (x=0) = 0 , which implies that A L + B L = 0 and hence ) sin( 2 ) ( ) ( kx i A e e A x L ikx ikx L L = = ψ Reflection Probability: The reflection probability is 1 | | | | 2 2 = = = L m k L m k L L R A B j j P h h r s . The transmission probability,
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: P T , is defined by P T = 1-P R = 0 . Probability Density: ) ( sin | | 4 | ) , ( | ) ( 2 2 2 kx A t x x L L L = Ψ = ρ , which is the same answer as taking the limit r → ∞ in the previous problem. ) ( sin | | 4 )) 2 cos( 1 ( | | 2 ) 2 sin( 1 2 ) 2 cos( 1 ) 1 ( 2 2 | | ) ( 2 2 2 2 2 2 2 kx A kx A kx r r kx r r A x L L r L L = − → + − + − + = ∞ → x x 0 = 0 E Infinite Step Potential Forbidden Region V= ∞ Step Potential: V = infinite-8-6-4-2 2 x Probability Density Max destructive interference!...
View Full 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