# Difference between revisions of "NucPhys I HomeworkProblems"

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:<math>V(x) =\left \{ {-V_0 \;\;\;\; 0<x <a \atop 0 \;\;\;\; x>a} \right .</math> | :<math>V(x) =\left \{ {-V_0 \;\;\;\; 0<x <a \atop 0 \;\;\;\; x>a} \right .</math> | ||

− | V_0 > 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. | + | <math>V_0 > 0</math>. 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 | 3.) Given the following barrier potential |

## Revision as of 17:48, 25 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:

. Assume particles are incident from , don't try to normalize but do express the wave function in terms of one coefficient.

3.) Given the following barrier potential

show that the transmission coefficient is

when

Assume particles are incident from

and .4.) Starting with Shrodinger's time-independent equation, derive the wave functions for a 2-D simple harmonic oscillator. Your derivation should take advantage of separation of variables and you are not required to normalize the wave function.

5.) Several nuclei decay by the emmission of an alpha particle. An alpha particle (He-4) is a tighlty bound nuclear containing 2 protons and 2 neutrons in which the energy needed to remove one neutron is 20.5 MeV. One model for this decay process views the alpha particle as being bound to the nucleus via a spherical potential well.

Once outside the nucleus, the alpha particle is repelled via Coulombs law

The original nucleus had a charge

and the alpha particle has a charge .Use the WKB approximation to show that the transmissivity (T : transmission coefficient) is:

- Media:GamowFormula.pdf Gamow's formula

where

- and and .