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bio website joshphysics.com
location Los Angeles
age 28
visits member for 1 year, 11 months
seen 5 mins ago

New project: phermi.com

Let me know if you know of any hard physics problems with clever solutions. (email listed to the left)

Personal website: joshphysics.com

Currently a lecturer at the UCLA Department of Physics and Astronomy.

Ph.D. theoretical high energy physics, UCLA.

BA/BS in physics/math, UC Berkeley.


1d
comment Schroedinger Equation and Special Relativity
@annav The equation $i\hbar d|\psi\rangle /dt = H|\psi\rangle$ is relativistic in the sense that it determines time evolution of every quantum system, including any relativistic systems such as those described by the standard model of particle physics. I'm rather confused by what exactly you desire. What sort of "demonstration" do you want? I agree that the equations $-(\hbar^2/2m)\nabla^2\psi + V\psi = E\psi$ and $-(\hbar^2/2m)\nabla^2\psi + V\psi = i\hbar \partial\psi/\partial t$ describe non-relativistic systems. (a non-rel massive particle) if that's what you're getting at.
1d
comment Schroedinger Equation and Special Relativity
@CuriousOne I think that might be a bit unfair to Tong in the sense that taken out of context, one might interpret the quote in the way you seem to be. Tong is referring specifically to time evolution, and if you ask me, it's quite conceptually important to emphasize that there's nothing new in QFT when it comes to time-evolution. I say this partly because more generally, it's important to realize that QFT is a model within the framework of quantum mechanics, and noting that quantum time evolution is adopted in exactly the same way is an important component of emphasizing that fact.
1d
comment Schroedinger Equation and Special Relativity
@CuriousOne That may be so, and if it is so, then I agree with you, but I'm not convinced that's the context the OP has in mind. Maybe the OP will grace us with clarification.
1d
comment Schroedinger Equation and Special Relativity
Any book on relativistic QFT will suffice since the starting point for time evolution is to use some "picture" (e.g. Schrodinger, Heisenberg, Interaction) all of which are equivalent to Schrodinger evolution. But for skeptics, see David Tong's QFT lecture notes equation 2.3 damtp.cam.ac.uk/user/tong/qft/two.pdf, and the surrounding quote: "All time dependence sits in the states which evolve by the usual Schrodinger equation. We aren’t doing anything different from usual quantum mechanics; we’re merely applying the old formalism to fields."
1d
comment Schroedinger Equation and Special Relativity
@CuriousOne The Schrodinger equation for time evolution, namely $i\hbar d|\psi\rangle/dt = H|\psi\rangle$ is not non-relativistic. In fact, it is the basis of time evolution in any quantum theory of anything, including QFT. Sorry to belabor the point, but I feel that this is one of those misconceptions that needs to be squashed rather assertively.
1d
comment Schroedinger Equation and Special Relativity
That doesn't narrow it down I'm afraid. There are two garden-variety equations that go by that name: $i\hbar d|\psi\rangle/dt = H|\psi\rangle$ and $-(\hbar^2/2m)\nabla^2\psi + V\psi = E\psi$. The former is relativistic, but the latter is not.
1d
comment Schroedinger Equation and Special Relativity
-1 (at least for now on answer (v1)): It's unclear to me which Schrodinger equation the OP is referring to. If the OP is referring to the Shrodinger equation for time evolution, then there is nothing non-relativistic about it; it is, in fact, completely fundamental and generally applies to all quantum systems. I think it's very important to make that clear.
1d
comment Schroedinger Equation and Special Relativity
Clarification on question (v1): Are you referring to the Schrodinger equation for time-evolution for "time independent Shrodinger equation" which is unfortunately named since it's really just the equation obeyed by energy eigenvectors? The former is fully general and relativistic.
1d
comment Is gravitational Chern-Simons action “topological” or not?
Closely related: physics.stackexchange.com/q/56211, physics.stackexchange.com/q/28888
2d
comment Mass particle trajectory on a sphere
@Alej Sure thing. In that case, it's a bit trickier because only removing the condition $\dot r = 0$ will just change the right hand sides of the coupled ODEs to include $r$, and one will now have two ODEs in three unknown functions. The way I would probably approach it would be to keep the analysis as is, determine when $N=0$ (since that's when it flies off the surface), and then a simple projectile motion problem remains. Otherwise, I'm not sure how to cleanly deal with the (non-holonomic) constraint $r\geq R$ instead of $r=R$.
2d
comment Canonical Distribution (Partition Function)
@user201175 I edited the answer and included a link at the end which might also be helpful.
2d
revised Canonical Distribution (Partition Function)
added 255 characters in body
2d
comment Canonical Distribution (Partition Function)
Yup! That's exactly right.
2d
comment Canonical Distribution (Partition Function)
Actually the point is that the two expressions (sum over states and sum over levels) are the same and completely general. You can sum over states without degeneracy factors, or you can sum over levels with degeneracy factors. Both forms give precisely the same number and work for arbitrary systems with discrete energy spectrum.
2d
answered Canonical Distribution (Partition Function)
Dec
15
comment Physical examples where changing the order of limits yields wrong result
Comment on answer (v2): Peter Shor not Pedro Shor.
Dec
14
answered Equivalence classes in a Hilbert space
Dec
13
awarded  Enlightened
Dec
13
awarded  Nice Answer
Dec
10
answered Mass particle trajectory on a sphere