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Nov
22
comment Why use a particular regularization for $\int_0^\infty \mathrm{d}x\,e^{i p x}$?
Alright, so limits and integrals don't commute in general. But then I guess the OP's asking how does one decide what value to assign to the integral above, since there are many different non-equivalent choices, as he has demonstrated.
Nov
22
comment Why use a particular regularization for $\int_0^\infty \mathrm{d}x\,e^{i p x}$?
@DavidZ I think Peter's point is that both integrands are equal to $e^{ipx}$ when you let $\varepsilon \rightarrow 0$.
Sep
9
comment Does one really need classical physics in order to understand quantum physics?
You don't necessarily need to know whats usually covered in "freshman physics". Instead, given your good math background, I would learn a few essential topics of classical mechanics mainly Lagrangians and Hamiltonians, from a sophisticated textbook. Landau and Lifschitz or Goldstein might be decent as they are commonly used in physics, though I haven't looked at either in a lot of detail. Another very concise but good book which covers classical mechanics, QM and QFT from a mathematician's perspective is by Dimock, called Quantum Mechanics and QFT, a mathematical primer.
Jul
22
awarded  Yearling
May
5
awarded  Notable Question
Apr
20
revised Converting between (abstract) linear operators and their position representations
added 2 characters in body
Apr
20
answered Converting between (abstract) linear operators and their position representations
Jan
30
comment Curvature of Spacetime
Also, relativity can be especially confusing and misleading without the math. Things like the twin paradox are essentially the result of the confusion caused by muddling conceptual phrases like "a moving clock works slower" and the precise mathematical equations. There is no paradox if you formulate the problem and subsequently solve it using just the precise mathematics.
Jan
28
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
... and if you get to that, do post it here as an answer, as I'd also be curious to see what it looks like. If you have any questions about this particular process, don't hesitate to ask.
Jan
28
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
Also note that since your Hilbert space $2^N$ dimensional, a general state could have just as many terms. So even for small $N$, your ground state could look very terrible and have lots of terms. I say this since it's often a misconception when doing many spins that a state is decomposable or has a simple form where some spins are up and others are down. If you really are bent on it, I'd try working it out explicitly for some low dimensional cases like $N = 2$, $3$ etc, in which case you could just write out a matrix for the Hamiltonian and use a computer to find your ground state....
Jan
20
comment Proving Lorentz invariance of Maxwell equations
Well firstly, it would be difficult to teach the most sophisticated version to people who are just starting out their undergraduate careers in Physics. Seeing how the electric and magnetic fields behave physically is also much clearer if you write them in terms of vector calculus notation.
Jan
20
comment Proving Lorentz invariance of Maxwell equations
Yes. You can write Maxwell's equations in terms of differential forms as well. This equation is simply $dF = 0$ in that notation.
Jan
20
comment Proving Lorentz invariance of Maxwell equations
Webb, the equation of the OP isn't derived from that Lagrangian however. That's the Bianchi identity and holds as soon as you say that your field strength $F$ is derived from a potential. $\mathcal{L}_{EM}$ gives you the other equation $\partial_{\mu}F^{\mu \nu} = 0$, if I'm not mistaken.
Jan
20
answered Proving Lorentz invariance of Maxwell equations
Jan
12
comment Generalized tight-binding model - how to solve it?
Are you familiar with how to solve the $\chi_{r,r+1} = 1$ case?
Jan
11
answered Kähler and complex manifolds
Jan
5
revised Canonical momentum density vs. energy-momentum tensor
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Jan
5
awarded  Critic
Jan
5
comment Trouble with classical mechanics self-learning (How to avoid going down the Physics rabbit hole?)
Rudin's PMA? Honestly? What one needs for basic physics is Stewart-style Calculus, namely a hueristic idea of what limits, derivatives and integrals are, and how to do effective computations with them. Most practicing physicists will never need the proofs of the Heine-Borel and Baire Category theorems in their entire career. Let alone someone who is just starting to self study Newtonian mechanics.
Jan
5
answered Canonical momentum density vs. energy-momentum tensor