{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

852_2010hw10 - PHYS852 Quantum Mechanics II Spring 2010...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
PHYS852 Quantum Mechanics II, Spring 2010 HOMEWORK ASSIGNMENT 10 Topics covered: Green’s function, Lippman-Schwinger Eq., T-matrix, Born Series. 1. T-matrix approach to one-dimensional scattering: In this problem, you will use the Lippman- Schwinger equation | ψ i = | ψ 0 i + GV | ψ i , (1) to solve the one-dimensional problem of tunneling through delta potentials. Take ψ 0 ( z ) = e ikz , and let V ( z ) = ( z ) + ( z - L ) . (2) (a) Express Eq. (1) as an integral equation for ψ ( z ), and then use the delta-functions to perform the integral. It might be helpful to introduce the dimensionless parameter α = Mg ~ 2 k . To solve for the two unknown constants, generate two equations by evaluating your solution at z = 0, and z = L . (b) Compute the transmission probability T = | t | 2 , with t defined via lim z →∞ ψ ( z ) = te ikz . (3) (c) In the strong-scatterer limit α 1, at what k -values is the transmission maximized? (d) Consider an infinite square-well of length L . What are the k -values for each bound-state? How do these compare with the transmission resonances in the strong-scatterer limit?
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}