Recent content by confused_man

My understanding is that you can describe the complicated motion of atoms in a crystal as a sum of standing waves (normal modes). A phonon is an excitation of a normal mode in the sense that it increases the vibration amplitude of that normal mode and the energy of that mode by a quantized...

Thank you to everyone for your replies. Sorry it took me a while to check back in. I understand the interference part very well, and that we get a diffraction pattern at very specific angles because of how the thousands of planes lead to destructive interference unless Bragg's condition is...

I'm reading about x-ray diffraction in the context of crystal structure determination. Usually this discussion begins with Bragg's law, $$2d\sin\theta=n\lambda,$$ where ##\theta## is the angle of incoming and "reflected" x-rays. This is the bit that bothers me. I understand that the...

I initially started getting confused about this when thinking about phonons. A single phonon is an excitation of a single mode with frequency ##\omega##. In a crystal, there are a vast number of phonons corresponding to the excitations of multiple modes of different frequencies. The number...

I'm trying to wrap my head around the dispersion relation ##\omega(k)##. I understand how you can construct a wavepacket by combining multiple traveling waves of different wavelengths. I can then calculate the phase and group velocities of this wavepacket: \begin{align*} v_p &=...

Thank you for the reply. What about the phase shift due in the transmitted beam due to the plate thickness? This is the one that I am confused about, as it seems that many sources just ignore the fact that the beam splitter has some finite width, which would introduce some additional phase...

I'm having trouble understanding the phase shift produced by a beam splitter. I seem to be finding conflicting information. I'm specifically looking to understand a 50/50 beam splitter where one side has a dielectric mirror, as shown in this figure from wikipedia: I understand the pi...

I'm trying to figure out how you would actually measure the result of a quantum gate. For example, suppose I build a Hadamard gate by using a beam splitter. The output of this gate creates either |\psi> = \frac{1}{\sqrt{2}} |0> + \frac{1}{\sqrt{2}} |1> or |\psi> = \frac{1}{\sqrt{2}} |0> -...

Hi everyone, This might belong in the quantum mechanics section, so I apologize if I placed this thread in the wrong place. My question is: how do I calculate the gradient of a multiparticle wavefunction? For example, suppose that a wavefunction \psi describing the probability...

Here's a better question: how can 100% of He4 atoms be in a superfluid state when T~0 K, while < 10% are Bose condensed? What makes the other 90% superfluid?

Hi Creator, That's a nice detailed post. Thanks! If I correctly understand what you are saying, the superfluid properties of He4 is due to it Bose condensing at temperatures below the lambda point (T = 2.17 K). It it then clear how the quantized vortices come about. In reality...

Thanks for your reply. I guess what I'm asking is when does a Bose gas cease to be irrotational. For example, at around 2 K, 4He is a superfluid but only around 7 percent of the atoms are Bose condensed. Suppose that you had a Bose gas that was slightly above the transition temperature...

Thanks Cthugha for pointing that out. I can't believe that was my mistake... In my defense, it was pretty late and I was tired! Since I can't edit my post anymore, here's the middle part: This can be shown by using the continuity equation for the probability density n , \frac{\partial...

Hmmm... It does not look like my latex code worked. I'm not sure why---I followed the instructions. Sorry about that!

Hello everyone, I'm trying to understand quantized vortices in rotating Bose gases. From what I understand, any system that is described by a quantum mechanical wavefunction [tex] \psi [\tex] will be irrotational (in other words, will only be able to get angular momentum through the...