# Chapter 2

## Set 1

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.

## Set 2

1.) Given the following barrier potential

show that the transmission coefficient is

when

Assume particles are incident from and .

## Set 3

1.) 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.

## Set 4

1.) Show that the mean-square charge radius of a uniformly charged sphere is

2.) Using the definition of the form factor and probably an integral table, caluclate when

a.)

b.)

c.)

## Set 5

2.) Muonic X-rays a.) Calculate the energies of muonic K-line X-rays from Fe assuming a point nucleus and using a one-electron model.. b.) Calculate the energy correction (\Delta E)

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:

Gamow's formula Media:GamowFormula.pdf

where

and and .