Scattering Theory and Quantum Transition

PHYSICS TEST ASSIGNMENT

The test paper is divided into two sections: Total Marks - 50

Section 1: Numerical – 20 Marks Section 2: Theoretical – 30 Marks

Section 1- Numerical

1. There is an outbreak in the ABC Bank. The robbers have a high end getaway car. They

escape in their car at a speed of 0.75c. The police has a pursuit car. The officer upon

seeing the robbers flee, fires a bullet from his car. The bullet goes just at a speed of 0.5c.

The relative velocity of the muzzle with respect to the gun is . Determine whether the

bullet reaches the getaway car according to (a) Galileo, (b) Einstein.

2. Consider the following fact:

The space charge in a beam causes a potential difference between axis and surface of

beam .

Now, a beam of protons (v = 3×10 6 , 10mA and 50 k-eV) moves along the axis of

evacuated beam pipe. Assume the beam to be with a circular cross-section (1cm

diameter). Also assume that the current density is uniform over the beam diameter.

Using the above data, we find that the potential difference between the axis and surface

of beam to be k V.

Then, the value of 𝑘 is?

Section 2- Theoretical

1. We have a spin-one-half projectile (mass m, Energy E = ℎ2𝑘2𝑚 ). This projectile scatters

a spin-one-target of infinite mass.

For this, the Hamiltonian is: ∫ = 𝐴𝜎 𝜎 𝑒−𝜇𝜏𝜏𝐻 In the above expression, µ > 0, σi represent the Pauli spin operators, where for i=1, we have the spin operator for projectile and for i=2, we have spin operator for

target.

Evaluate 𝜃Ω (differential scattering cross section), in lowest order Born

approximation. The same should be calculated as a function of k and scattering

angle. Also, computation should be done averaging over initial; and summing over

final states of spin polarization.

The write up should include the following parts:

a. Title Page

b. Table of Contents

c. Abstract

d. Background

e. Introduction

f. The Problem Statement and Data given

g. Assumptions (if any)

h. Computation with necessary explanations

i. Conclusion and Inference

j. References

k. Appendices

There should be minimum 4 academic references in APA Style.