I have never seen the Taylor expansion written like this, and I still don't see the reason for multiplying two vertical displacements, or even doing a Taylor expansion in the vertical direction, if there is no spring in the vertical direction in the first place..
Do you remember this form of...
Also, I don't really understand how a 2D lattice is supposed to be motivation for a 3D field. We should have a 3D lattice with springs in every direction (x,y,z), and the particles should be free to move horizontally and vertically, not just mostly vertically. And who says a spring can't...
Ok sure, but I still don't understand what the product q_a*q_b means. Why on Earth would we multiply the vertical displacements of two consecutive particles? This doesn't give anything physically meaningful.
Just started with QFT from Zee and am already confused by first equation lol. See attached picture. Does anyone actually understand this? He calls q_a the vertical displacement of particle 'a', and yet he only allows the springs to be horizontally between the particles. So, there should be...
[A,B] = AB-BA, so the commutator should be a matrix in general, but yet
[x,p]=i*hbar...which is just a scalar. Unless by this commutator, we mean i*hbar*(identity matrix) ?
I am asking because I see in a paper the following:
tr[A,B]
Which I interpret to mean the trace of the commutator...
Here you go. I uploaded the relevant part of the derivation from Sakurai's Modern QM book, and the eqn 1.4.53 he refers to (which is just the general uncertainty principle). I don't think it is a linguistic issue, though I may be wrong.
You will notice there is a footnote referred to...
Thanks! haha wow first time I am 'right' here!
Sakurai also says dropping the term makes the relation stronger. That is where I first saw this, and didn't think it possible for this quantum god to be wrong lol.
In the derivation of the generalized uncertainty principle (as pgs 1-2 of here), there is an anticommutator term that is dropped at the end, leaving just the commutator part...this is said to "strengthen" the relation, as both terms are positive.
I don't understand this. So we basically have...
I know that SO(n) means a rotation in n dimensions, but sometimes I see a second index, such as SO(n,p). What does p mean? I cannot find much resources on this.
In vector form,
L=Iω.
I am trying to show that for a point particle, this reduces to L=rxp, but am getting an extra factor of r2 :
For the case of a point particle, I=Mr2.
Also, ω=rxv.
Plugging these into L=Iω gives:
L=Mr2(rxv) = r2(rxp).
Thus this reduces to a point particle...
Problem from past PGRE:
A particle of mass m moves in a one-dimensional potential V(x)=-ax2 + bx4, where a and b are positive constants. The angular frequency of small oscillations about the minima of the potential is equal to:
Answer is 2(a/m)1/2.
I understand how this is found 'the long...
In a past physics gre question (https://www.physicsforums.com/showthread.php?t=192334), we make use of the idea that the ground state energy of two ions that have spin is when the spins are aligned.
However, the ground state of the helium atom is a spin singlet state, which is a linear combo...
This may be a stupid question, but I am reviewing for the physics gre and can't help but see the zeeman effect and stern-gerlach experiments as contradictions. In the Zeeman effect, a neutral atom energy level will split into 3 levels (or 2 or more if take into account anomalous zeeman), but in...