Penetrating the Rectangular Potential Barrier, E < V0

  • Thread starter Chip
  • Start date
  • #1
30
1

Homework Statement


Rectangular barrier of width a and height V0 with an E < V0. What is the transmission ratio, T?

Homework Equations


T = C*C/A*A
What am I missing in my attempted solution (variable name = TChip), which is different from the known solution (variable name = TSoln)?

The Attempt at a Solution


(shown in the Octave code below...note the actual solution has a negative concavity, whereas my solution has a positive concavity, but seems to be in the vicinity of the correct solution...this can be seen by running the Octave code).

****

%I wrote this to check my work thus far on solving the GIANT algebra problem of penetrating the rectangular barrier, where E < V0
clear;close;clc;
% setting some constants

hbar = 1.0545718*10^(-34);
m = 9.10938356 * 10^(-31);
a = 10^-20; %cab be purely arbitrary

V0 = 100; %cab be purely arbitrary
inc = 10;
E = inc:inc:(V0-inc);

%wavenumber formulas
k1 = (sqrt(2*m*E))/hbar;
k2 = (sqrt(2*m*(V0-E)))/hbar;

%this section contains the solution
TSoln = (1 + (((sinh(k2*a)).^2)./((4*E/V0).*(1-E/V0)))).^(-1)

%this section contains my work thus far

iVal = i*k2/k1;
BLABLA1 = ( 1 - ((1-iVal).*(e.^(-2*k2*a) )./(1+iVal) ) ) + iVal.* (1 + ((1-iVal).*(e.^(-2*k2*a) )./(1+iVal)));
BLABLA2 = ( 1 - ((1+iVal).*(e.^(2*k2*a) )./(1-iVal) ) ) - iVal.* (1 + ((1+iVal).*(e.^(2*k2*a) )./(1-iVal)));

C = (e.^(-i*k1*a)).* ((e.^(-k2*a)./ ( BLABLA1 ) ) + (e.^(k2*a)./ ( BLABLA2 )));
TChip = 4*(C.*conj(C))

plot (E, [TSoln;TChip]);[/B]
 
Last edited:

Answers and Replies

  • #2
18,354
8,163
Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
30
1
Well, maybe I just need to work side my side with someone on this. I just can't seem to get to the answer..
 

Related Threads on Penetrating the Rectangular Potential Barrier, E < V0

Replies
6
Views
5K
  • Last Post
Replies
2
Views
3K
Replies
1
Views
883
Replies
1
Views
2K
Replies
4
Views
619
  • Last Post
Replies
2
Views
8K
  • Last Post
Replies
4
Views
6K
Replies
2
Views
5K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
0
Views
2K
Top