Recent content by pai535

I think in your case if you don't consider absorption, only part of the light interferes and the residual light is transmitted through the mirror. If two waves with the same frequency but different amplitudes interfere, there will be a wave after interference even if the interference is destructive.

After you change your variable, the upper limit of integral will be ##\hbar\omega_D/k_B T##. Then put ##T\to 0## so ##\hbar\omega_D/k_B T \to \infty## and integrate. For high-temperature behaviour, ##T \to \infty##, ##\hbar\omega/k_B T \to 0##. In this case maybe you don't change your variable...

Although I've never learned about Lorentzian profile, I'd like to have a guess. $$L = \frac{1}{1+2(\frac{\omega - 17\,KeV/\hbar}{0.1\,eV/\hbar})^2}$$ This profile is just a function of ##\omega##. First we have a series of ##\omega## range from 0 to ##\infty## and can generate a profile (a...

I'd like to add: I think that it is easier to figure out what is "proper" - time or length (of "something") can be called "proper" when it is measured by an observer who is at rest w.r.t. (that "something"). Proper time is shortest time interval, while proper length is longest length. Given...

Just think of an apparatus that if you send in a beam of charged particles, only the ones with a specific speed can travel through. Then you can sort out all the particles with the speed you want (by adjusting E and M fields).

Actually LaTeX is everywhere in science, not just physics. If you want to write and publish scientific articles (and even books), you'd better learn some LaTeX. Probably there will also be formulas and calculations in your future study (although I don't know much about chemistry). Using LaTeX...

Using the ratio, you can express ##v_y## in terms of ##v_x## (also ##v_x## in terms of ##v_y##). Then you reduce the problem to a problem with only one unknown variable.

If you want to know how to get Helmholtz from diffusion equation, this is what you want. You only need to figure out how you can transform the above equation into the form of Helmholtz. If you want to solve the Helmholtz equation, I will give a hint in Cartesian coordinates. Do separation of...

In my perspective, in reality it is not even possible to say that a data set is "continuous" - because there is an infinite number of real numbers between all two data in a data set. I think the meaning of "continuous" here is that if you have a probability distribution function, then the...

For this question, you only need to give the equation (and maybe don't need to solve it). For Helmholtz equation, you can solve it by separation of variables.

Seems like your question doesn't ask you to solve the equation. If you really want to solve a differential equation, you can manipulate it to look like Helmholtz, because it is easy to solve Helmholtz equation (Your teacher told you the formal solution, didn't he?). This also applies to other...

Wow, sounds interesting. I'll watch it sometime. :biggrin:

I don't know. Google says it is from Real Genius.:biggrin:

I just finished my undergrad months ago and I felt good and bad to find here. Feeling bad because I didn't find this forum in my undergrad years, and studying physics gave me so much trouble. Feeling good because this is such an awesome place with various kind of topics. I cannot wait to read...

You made a mistake in this calculation of cross product. Maybe you can write down the determinant explicitly and try to figure out what are the components. There is another hint in your question that you didn't use - the velocity is perpendicular to magnetic field. As mentioned above, you will...