Difference between revisions of "NucPhys I HomeworkProblems"

From New IAC Wiki
Jump to navigation Jump to search
Line 10: Line 10:
 
V_0 > 0 and E>0.  Assume particles are incident from <math>x = -\infty</math>, don't try to normalize but do express the wave function in terms of one coefficient.
 
V_0 > 0 and E>0.  Assume particles are incident from <math>x = -\infty</math>, don't try to normalize but do express the wave function in terms of one coefficient.
  
 +
3.) Given the following barrier potential
 +
 +
:<math>V(x) = \infty \;\; x<0</math>
 +
:<math>V(x) =\left \{  {V_0 \;\;\;\; 0<x <a \atop 0 \;\;\;\; x>a} \right .</math>
 +
 +
show that the transmission coefficient is
 +
 +
: T = \frac{1}{1+ \frac{v_o^2 \sinh^2(k_2a)}{4E(V_o-E)}}
 +
 +
when <math>E < V_o</math>
 +
 +
Assume particles are incident from <math>x = -\infty</math> and <math>k_2^2 = 2m(V_o-E)/\hbar^2</math>.
  
  
 
[http://www.iac.isu.edu/mediawiki/index.php/Forest_NucPhys_I Go Back]
 
[http://www.iac.isu.edu/mediawiki/index.php/Forest_NucPhys_I Go Back]

Revision as of 16:56, 6 February 2008

Chapter 2

1.) In your own words, describe what the "Standard Model" of physics is using 2 to 5 paragraphs. Your paragraphs should include the concepts of the 4 fundamental forces of physics, QED, and QCD at a minimum. Any sentences in which a string of 5 or more words match a sentence that is found on the internet will be evidence of cheating.


2.) Solve the Schrodinger equation for the following potential:

[math]V(x) = \infty \;\; x\lt 0[/math]
[math]V(x) =\left \{ {-V_0 \;\;\;\; 0\lt x \lt a \atop 0 \;\;\;\; x\gt a} \right .[/math]

V_0 > 0 and E>0. Assume particles are incident from [math]x = -\infty[/math], don't try to normalize but do express the wave function in terms of one coefficient.

3.) Given the following barrier potential

:[math]V(x) = \infty \;\; x\lt 0[/math]
[math]V(x) =\left \{ {V_0 \;\;\;\; 0\lt x \lt a \atop 0 \;\;\;\; x\gt a} \right .[/math]

show that the transmission coefficient is

T = \frac{1}{1+ \frac{v_o^2 \sinh^2(k_2a)}{4E(V_o-E)}}

when [math]E \lt V_o[/math]

Assume particles are incident from [math]x = -\infty[/math] and [math]k_2^2 = 2m(V_o-E)/\hbar^2[/math].


Go Back