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### Problem/QFT-15011 Rutherford Scattering in Second quantized Schrodinger equation

Write the Lagrangian for a nonrelativistic particle moving in  a potential  $$V(r)$$. Using the second quantized formalism compute the scattering cross  section in the lowest order in the potential. Show that this result is same as the first Born approximation expression in nonrelativistic, first quantized formulation of quantum mechanics. Taking V(r) as Coulomb potential obtain the Rutherford formula:$\left(\frac{d\sigma}{d\Omega}\right)_\text{R} = \frac{Ze^2}{64\pi m^2v^4 \sin^4(\theta/2)}$

kapoor 24/02/19

### Problem/QFT-15006 Relativistic Coulomb scattering of Dirac Particle

Write Dirac equation in external electromagentic potential  $$A_\mu(\vec{x})$$. Assume the potentials for Coulomb interactions with a nucleus of charge $$Ze$$ to be
$\vec{A}=0, \quad A_0 = \frac{Ze}{4\pi |\vec{x}|}.$
Show that the differential cross section for electron scattering from nucleus is
given by
$\frac{d\sigma}{d\Omega}= \left(\frac{d\sigma}{d\Omega}\right)_\text{R} \Big(1-v^2\sin^2(\theta/2)\Big)$ where
$\left(\frac{d\sigma}{d\Omega}\right)_\text{R} = \frac{Ze^2}{64\pi m^2v^4 \sin^4(\theta/2)}$
is the Rutherford cross section for nonrelativistic Coulomb scattering.

kapoor 24/02/19

### Problem/QFT-15010 $$\pi^+-\pi^0$$ scattering

Assuming interactions of charged pions to be of the form $$\scr{L}_\text{int} (x)= (g/4)(\pi(x)^+\pi(x)^0)^2$$  find

1. the $$S$$ matrix element for $$\pi-\pi$$ scattering         $\pi^+ + \pi^0 \longrightarrow \pi^+ + \pi^0$
2.  transition probability per unit time per unit volume for $$\pi - \pi$$  scattering.
3. Compute the total cross section for the scattering process and show that
$\frac{d\sigma}{d\Omega}= \frac{g^2}{64\pi^2 E_\text{cm}^2}$
kapoor 24/02/19

### Problem/QFT-15009 Charged pion, ((\pi^+, \pi^-)\), scattering

Assuming interactions of charged pions to be of the form $$\scr{L}_\text{int} (x)= (g/4)(\pi(x)^+\pi(x)^-)^2$$  find

1. the $$S$$ matrix element for $$\pi-\pi$$ scattering $\pi^+ + \pi^-\longrightarrow \pi^+ + \pi^-$
2. transition probability per unit time per unit volume for $$\pi - \pi$$ scattering.
3. compute the total cross section for the scattering process and show that      $\frac{d\sigma}{d\Omega}= \frac{g^2}{64\pi^2 E_\text{cm}^2}$
kapoor 24/02/19

### QFT/17- Course Overview

Summary (or abstract) not available for this node.
kapoor 24/02/19

Summary (or abstract) not available for this node.
kapoor 22/02/19

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kapoor 22/02/19

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kapoor 22/02/19

### From Masters : "Do not remain nameless ... " Feynman

Summary (or abstract) not available for this node.
kapoor 22/02/19

kapoor 22/02/19