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_0 \;\;\;\; 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].

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