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\(\S\S\) 3.6 :: Discontinuity across the branch cut

The solutions for probblems in chapter 3 appear here. To go to  desired section expand the Table of Contents by clicking there. 

 

kapoor kapoor's picture 01/03/19

\(\S\S\) 3.2 :: Tutorial ---The square root branch cut

Summary (or abstract) not available for this node.
kapoor kapoor's picture 01/03/19

\(\S\S\) 3.1 :: Questions ----------- Branch Point

Summary (or abstract) not available for this node.
kapoor kapoor's picture 01/03/19

Is it difficult to share learning content?

No, if it is already published on Internet.

Yes, if it is mine and is in PDF/DOC/PPT format.

ranjan ranjan's picture 01/03/19

Repository of Lecture Notes (All Areas) :: Top-Page

 Quick Help :: Navigation                                               \(\triangleright\) Book: Table of Contents  (top line) can be expanded; Learn How to 

kapoor kapoor's picture 28/02/19

Classical Mechanics :: Lecture Notes == Home-Page

 Quick Help :: Navigation                                               \(\triangleright\) Book: Table of Contents  (top line) can be expanded; Learn How to 

kapoor kapoor's picture 28/02/19

Repository of Questions and Problems (All Areas )

 Quick Help :: Navigation                                               \(\triangleright\) Book: Table of Contents  (top line) can be expanded; Learn How to 

kapoor kapoor's picture 28/02/19

QM-05031 :: Temperature of Sun

Consider an ionised plasma of protons in thermal equilibrium. Assuming a Maxwell-Boltzmann distribution, estimate the temperature required for two protons to overcome the Coulomb barrier for fusion assuming an approach distance of 1 fm. Compare this with the temperature when quantum effects come into play. For this, use the distance between the two protons as the de-Broglie wavelength at which Coulomb energy becomes equal to the kinetic energy of the protons.  

See attached document for solution.

kapoor kapoor's picture 28/02/19

QM-13001 :: Car on a Ramp

Consider a one dimensional motion of a particle along the x-axis under the action of a potential $V(x)=V_0>0$ for $x<=0$ and $V(x)=0$ for $x>0$. If the particle moves to the right from $x<0$, with an energy $2V_0$, standard quantum mechanics gives for the reflection coeffient at $x=0$ of the $0(1)$ ( The exact number is $(|(\sqrt{2}-1|/|\sqrt{2}+1|)^{1/2}$) and the result is independent of the mass of the particle.

Now consider a car travelling with a speed $v$ towards a cliff ( height $H$) as shown in the figure. From the previous calculation the probability of reflection at $x=0$ should be $0(1)$ ( Assume the kinetic energy of the car to be of the same order as $mgH$ where $m$ is the mass of the car.). This is an absurd result.Do a correct modelling for the cliff and obtain a physically reasonable result.
 Car on a Ramp 
kapoor kapoor's picture 28/02/19

Problem/QFT-15005 Charged pion decay \( \pi^- \to e^- \bar{\nu}\)


The interaction Hamiltonian for pion decay \(\pi^-\longrightarrow e^- +
\bar{\nu} \) can be written as \[H_\text{int} = \frac{g}{\sqrt{2}}\bar{\psi}_e(x)\gamma_\mu(1-\gamma_5)\psi(x)_\nu \partial^\mu \phi_\pi^-(x) + h.c. \]

  1. Show that the decay rate is given by \[\Gamma = \frac{g^2}{8\pi} \frac{m_e^2(m_\pi^2-m_e^2)^2}{m_\pi^3}.\]
  2. Assuming that the coupling constant for \(\pi^-\longrightarrow \mu^- +\bar{\nu} \) is equal to that for the electron decay, calculate the branching ratio \[\frac{\Gamma(\pi^-\longrightarrow \mu^- +\bar{\nu})} {\Gamma((\pi^-\longrightarrow e^- + \bar{\nu})} \]
kapoor kapoor's picture 28/02/19

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