Recent content by Riotto

For a system of interacting particles, is it possible to define single-particle phase spaces? If not, why?

Can you show a few lines of computation because I cannot figure out how are you getting that result. No, I am using $\alpha=1.$

Can you show a few lines of computation because I cannot figure out how are you getting that result. No, I am using ##\alpha=1## .

In David Tong's QFT notes (see http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf , page 131, Eq. 6.38) the expression for canonical momentum ##\pi^0## is given by ##\pi^0=-\partial_\rho A^\rho## while my calculation gives ##\pi^\rho=-\partial_0 A^\rho## so that ##\pi^0=-\partial_0 A^0##. Is it...

Can all differential equations be turned into algebraic equations by Fourier transform (FT)? If not, what kind of differential equations can be solved by the FT technique?

What's your objection to moving charges? Currents are produced by moving charges. In general, a given charge can also accelerate due to the forces experienced by the electric and magnetic field produced by the other charges.

Thanks for the help. :-)

Thanks A. Neumaier. So for problems which are not exactly solvable, and in which the 'unsolvable part' of the Hamiltonian is not "small", other nonperturbative approximation methods become useful for calculating energy eigenvalues and eigenfunctions. Do I get it right?

So nonperturbative methods are also approximation methods?

Even perturbation theory beyond a certain order will have to be dealt with numerically. Even when you don't use perturbation theory, your numerical algorithm must be based on some framework, some approximation method if not perturbation theory. The question is which framework(s) do people have...

Which method other than the perturbation theory should one apply in this example of yours? Do you have some other approximation method such as the variational principle in mind? Thanks!

Dear DrClaude, I appreciate your help but unfortunately, your answer didn't address my actual question. The question asks about an explanation for the nonperturbative approach of quantum mechanics and occasions when it becomes indispensable perhaps with an illustration. I'm aware of what is the...

No. It's not a homework. It's for my personal understanding. My exposure to quantum mechanics is that of the undergraduate level. Sorry for the advanced tag. Not a frequent user. Title changed now.

What is the nonperturbative approach to quantum mechanics as opposed to perturbative one? When does the latter method fail and one has to apply nonperturbative approach? Please keep your discussion confined within non-relativistic quantum mechanics.

You can't travel at 2c (twice the velocity of light in vacuum)! This violates the postulate of special relativity. Massive objects cannot even travel at the speed of light $c$. So you can modify your question to make it meaningful so that someone can help.