Recent content by Judas503

I'm seeking the solution to the following integro-differential equation: $$ \frac{\partial c(x,t)}{\partial t}=-xc(x,t)+2\int_{x}^{\infty} c(y,t)dy$$ I know that to solve this, the Laplace transform must be taken term by term. Let $$ \mathcal{L}\{c(x,t)\}=\int_{0}^{\infty}e^{-st}c(x,s) $$ Then...

Homework Statement I have the following massive spin-1 propagator- $$ D^{\mu\nu}(k)=\frac{\eta^{\mu\nu}-\frac{k^{\mu}k^{\nu}}{m^2}}{k^2 - m^2} $$ I want to write down the propagator in the imaginary time formalism commonly used in thermal field theories. Homework EquationsThe Attempt at a...

Yes, sorry! I forgot to put the "i" in the exponential form of sine. That should clear the problem.

Homework Statement The problem requires to solve the integration to find ## G(t) ## after ##G(\omega)## is found via Fourier transform. We have G(\omega)= \frac{1}{2\pi}\frac{1}{\omega _{0}^2 - \omega ^2} Homework Equations As mentioned previously, the question asks to find ##G(t)## The...

1. The problem is to find the series solution to the following differential equation $$ x^2 \frac{d^2 x}{dx^2}+x\frac{dy}{dx}+(x^2 - 1)y $$ 3. Using the ansatz $$ y = \sum _{\lambda = 0}^{\infty}a_{\lambda}x^{k+\lambda}$$ the solution to the indicial equation was found to be...

Griffiths' one is an easy read!

Hello there, I wanted to know whether the Ph.D qualifying exams have to be taken when a student begins grad school? In some university websites, it's mentioned that all incoming students need to sit for the exam before the begin classes (provided they have sufficient background). Some other...

In the answer, is \ddot{\theta}=\frac{2g\sin{\alpha}}{3r} ?

If you are careful with the manipulations of the operators, it's an easy problem.

First, if you assume the operator has an explicit time dependence, you can write: \frac{d}{dt}\langle \phi |A(x,t)|\phi\rangle = \langle \frac{d\phi}{dt}|A|\phi\rangle +\langle \phi|\frac{dA}{dt}|\phi \rangle +\langle \phi |A|\frac{d \phi}{dt}\rangle Then, the R.H.S. can be simplified to...

I encountered the following second order nonlinear ODE while solving a problem in electrostatics. The ODE is: \frac{d^{2}V}{dx^{2}} = CV^{-1/2} How can I solve this? Regards. Homework Statement Homework Equations The Attempt at a Solution

You could look into the Classical Mechanics lectures of Prof. V. Balakrishnan of IIT. They series constitutes of 38 lectures and covers Lagrangian and Hamiltonian mechanics with a lot of mathematical rigour. I'm sorry for not being able to provide the links since accessing youtube in my country...

Ok...thanks a lot

So, will there be any problem if GR is taken at a graduate level? Will there be sufficient time to cover all the concepts bearing in mind that grad physics courses have quantum field theory and relativistic quantum mechanics?

Hey there, In my university, General Relativity is listed among elective courses (along with an advanced quantum mechanics course). I'm curious to know whether general relativity is really an undergrad course or not. And what are the pros and cons if GR is taken in grad school? Thanks for...