# HW6 - Quantum Mechanics I Physics 3143 Assignment 6 Fall...

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

Quantum Mechanics I, Physics 3143: Assignment 6, Fall 2010 1 . Consider scattering from a step potential V ( x ) = 0 , x < 0; V 0 , x 0 . Suppose that incoming particles from x = -∞ , with energy E , are incident on the interface. Calculate the incident, reflected and transmitted particle currents in the case E > V 0 , and hence determine the reflection coefficient R from the barrier in terms of the wave numbers of the incident and transmitted particles, k 1 and k 2 , respectively. 2 . Make a sketch/plot of the potential V ( x ) = V 0 / (1 + e - x/l ), and state under what condi- tions the potential approaches the potential of problem 1. For the smoothly varying poten- tial Schrodinger’s time-independent equation may be solved exactly to yield the reflection coefficient R = sinh [ π ( k 1 - k 2 ) l ] sinh [ π ( k 1 + k 2 ) l ] 2 . (a) Discuss the limiting cases E = V 0 and E >> V 0 , respectively. (b) In the case E >> V 0 , R does not agree with the reflection coefficient found in the same limit in problem 1. What is the reason for this ?

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

View Full Document
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