NucPhys I HomeworkProblems
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]\displaystyle{ V(x) = \infty \;\; x<0 }[/math]
- [math]\displaystyle{ V(x) =\left \{ {-V_0 \;\;\;\; 0<x <a \atop 0 \;\;\;\; x>a} \right . }[/math]
V_0 > 0 and E>0. Assume particles are incident from [math]\displaystyle{ 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]\displaystyle{ V(x) = \infty \;\; x<0 }[/math]
- [math]\displaystyle{ V(x) =\left \{ {V_o \;\;\;\; 0<x <a \atop 0 \;\;\;\; x>a} \right . }[/math]
show that the transmission coefficient is
- [math]\displaystyle{ T = \frac{1}{1+ \frac{V_o^2 \sinh^2(k_2a)}{4E(V_o-E)}} }[/math]
when [math]\displaystyle{ E < V_o }[/math]
Assume particles are incident from [math]\displaystyle{ x = -\infty }[/math] and [math]\displaystyle{ k_2^2 = 2m(V_o-E)/\hbar^2 }[/math].