- #1

- 91

- 0

## Homework Statement

Transmission of a quantum mechanical wave past a one-dimensional square well results in the following expressions relating initial to final wave amplitudes:

[tex]A= (cos(2ka)-{i\epsilon\over2}sin(2ka))e^{2ia\lambda}F+{i\eta\over2}sin(2ka)G[/tex]

[tex]B= {-i\eta\over2}sin(2ka)F+(cos(2ka)+{i\epsilon\over2}sin(2ka))e^{-2ia\lambda}G[/tex]

[tex]\epsilon={\lambda\over(k)}+{k\over\lambda}[/tex]

[tex]\eta={\lambda\over(k)}-{(k)\over\lambda}[/tex]

For G=0 (this represents an initial beam coming in only from the left) the "transmission" and "reflection" coefficients are defined respectively as:

[tex]T=|{F\over(A)}|^2[/tex]

[tex]R=|{B\over(A)}|^2=1-T[/tex]

Show that

[tex]T={1\over(cos^2(2ka)+{\epsilon^2\over4}sin^2(2ka))}[/tex]

and

[tex]R={({\epsilon^2\over4}-1)sin^2(2ka)\over1+({\epsilon^2\over4}-1)sin^2(2ka)}[/tex]

## Homework Equations

See above

## The Attempt at a Solution

This is a "challenge" problem from my mathematical methods in physics class. I have faith in this class and I would like to ask for a hint. What I mean is that I believe this problem will give me greater insight into complex arithmetic as the other challenge problems have. I worked with my group members for a few hours last night and didn't get anywhere. Mainly we kept trying to re-write things in different terms to see if we could reach the desired result. I believe that we are not thinking about the "spirit" (as my professor calls it) of the question. That is we are not thinking about how this question relates to complex arithmetic. Any takers?

Thank you for taking the time to read this thread.

## Homework Statement

## Homework Equations

## The Attempt at a Solution

Last edited: