- #1

zZhang

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## Homework Statement

A particle of mass m and energy E, where E >V1 >V2 travels to the right in a potential defined as

V(x) = V1 for - b < x < 0

V(x) = 0 for 0 < x < a

V(x) = V2 for a < x < b

(a) Write down the time-independent Schrodinger eq. and its general solution in each region. Use complex exponential notation.

(b) Write down the boundary conditions which fix the undetermined constants in the solution of part (a).

(c) Eliminate from those eqs. The normalization for the wave in region 3 and calculate the ratio of intensities of waves traveling to the left and to the right in region number 2.

## Homework Equations

## The Attempt at a Solution

I really have no idea what I am doing. After writing the solutions as

ψ(x) = A*exp(ikx) + B*exp(-ikx) with appropriate k for each of the 3 situations,

I just cannot solve for the undetermined coefficients (and I've been doing this for the last 3 hours -_-). So yea, I'm completely lost.

EDIT: Boundary Conditions are

1)A$_{1}$e$^{-ik$_{1}$b}$ + B$_{1}$e$^{ik$_{1}$b}$ = 0

2)A$_{1}$ + B$_{1}$ = A$_{2}$ + B$_{2}$

3)k$_{1}$(A$_{1}$ - B$_{1}$) = k$_{2}$(A$_{2}$ - B$_{2}$)

4)A$_{2}$e$^{ik$_{2}$b}$ + B$_{2}$e$^{-ik$_{2}$b}$ = A$_{3}$e$^{ik$_{3}$b}$ + A$_{3}$e$^{-ik$_{3}$b}$

5)k$_{2}$(A$_{2}$e$^{ik$_{2}$b}$ - B$_{2}$e$^{-ik$_{2}$b}$) = k$_{3}$(A$_{3}$e$^{ik$_{3}$b}$ - B$_{3}$e$^{-ik$_{3}$b}$)

6)A$_{3}$e$^{ik$_{3}$b}$ + B$_{3}$e$^{-ik$_{3}$b}$ = 0

Look right to u guys?

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