Recent content by jrosen13

One step model is way better :)

The idea here seems to be that the very large energy density in the gravitational field would result in relatively large quantum fluctuations in mass density, and that perhaps these fluctuations in mass could effect some astrophysical phenomenon such as a star on the verge of supernova. The...

That was my feeling before, that numerically you can solve a cubic polynomial to whatever accuracy you desire, up to some fundamental limit of time cost perhaps, but that you should be able to get really close without too much trouble. However, it is possible to analytically solve it! e.g...

I just noticed you wrote your spring constant as a function of x, but that wouldn't be right, would it?

I would say that is a very crude model that doesn't explain many of the properties of conduction, for instance why does the rate of heat flow between two objects in contact depend on the pressure applied on the contact surface (and it definitely does). Why does a fairly good conductor transfer...

Conduction is not a microscopic idea, but a macroscopic one. These ideas were developed well before quantum mechanics ever existed, by observing large objects in contact with each other, or not in direct contact that still transfer heat. This was understood as radiation, which was an...

Mathematica would just give you the answer, Eigenvalues[matrix], done. To calculate yourself, sure get your cubic polynomial and figure out a way to solve it, numerically perhaps?

separation of variables to turn it into ordinary differential equations. It looks like __ equation for spatial part, and __ for time part, but I won't fill in the blanks, that's cheating :)

It wasn't so bad was it? That looks right to me, harmonic oscillator all the way. In the future try to realize if you are patient and think it through a little you will figure it out. Don't be in a hurry to get the answer, enjoy the process of figuring it out for yourself!

Sorry that was basically overkill, I had different idea in mind when i looked at it quickly before. Sketch the potential, where does the mass start out? Is it reasonable to approximate the potential by one that you know well?

Yep, you assume 100% detection efficiency in the detector (since you detect 50% right next to the source this is implied), which is basically never going to happen in real life due to charge leakage or readout noise and many other effects.

Looks like an instanton to me. Anyways, don't you just do the normal lagrangian/hamiltonian methods here? Its just a classical problem, right?

In physics, when one has a crazy idea that works, it may be necessary to state that it is not the only way to look at it so people don't simply dismiss it because it seems crazy. The essence is that the classical path is a stationary point of the action, i.e. a maximum/minimum/ or saddle point...

This is correct except you divided by two at the end. The question asks what fraction of the total radiation you detect. To do this absolutely correctly you are just talking about the solid angle that detector covers with the point source at the origin. At first it covers 2pi solid angle, so...

I think that in this forum there is really only so much you can say before it is like writing a book on the subject. Here we can only answer specific questions, but at some point people will need to open a standard textbook on the subject and get the hard facts. If there is still questions...