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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.
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
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
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.
Sep
18
comment In what sense is the path integral an independent formulation of Quantum Mechanics/Field Theory?
Sorry for that. I meant "we all know..." in the sense that it's the way a person familiar with the subject will traditionally think about things.
Jun
2
comment Problem with calculating the curvature tensor of the $n$ dimensional sphere
I should inform you that the equation you're using for the curvature tensor only holds in riemann normal coordinates and not in general. You should use the expression with the christoffels symbols.
Jun
2
comment What is the correct arrangement of the elements of Pauli matrices?
There would be no notable consequences, other than the headaches induced from matching up your algebraic signs with the ones found in textbooks and literature :). This would inevitable once you get to raising and lowering operators for AM.
Jun
2
comment Equation for null geodesic around schwarzschild metric?
You can find a treatment of this topic in any book on GR, in particular I liked Schutz's book, where he does this in chapter 11. IIRC, the idea is to recognize and exploit the constants of motion.
May
31
comment Why define four-vectors to be quantities that transform only like the position vector transforms?
Agreed, this is perhaps easier to digest for a new user. I must admit, I myself, do not understand very well the idea that "vectors are partial derivatives." My guess is that defining things in that manner makes the Jacobian transformation law fall out quite naturally, all while keeping the definitions very "mathy" (defining everything to be maps).
May
31
comment Proof that the Earth rotates?
Nothing too fancy, just basic differential geometry (parallel transport is the main concept used here, look it up). The kind you would learn in the first half of a general relativity class.
Jan
17
comment Pure mathematical exposition vs A “for physicists” approach: Which is better?
I personally think it could be the topic of a very productive discussion.
Jul
27
comment Advice on classes: Theoretical Mechanics vs E&M II
I certainly want to be learning QFT during my senior year. So do you think it's absolutely essential that I have stat mech before doing so or is it also doable concurrently?
Jul
27
comment Advice on classes: Theoretical Mechanics vs E&M II
Yes, for the first choice I'm mostly sure that I'll be doing mechanics. For the second one, I'm still thinking. I was considering math methods because I've taken or know the material to most of the applied math classes that the math department has to offer (calculus, ODEs, PDEs, complex variables etc) and still feel that there's a great deal to learn. You're correct in that grad-level algebra along with Grad Mechanics and Grad Quantum might be too much to handle so Stat Mech may be a good choice.
Jul
24
comment Lagrangian of two particles connected with a spring, free to rotate
Yes I got exactly this. Thank you too.
Jul
24
comment Lagrangian of two particles connected with a spring, free to rotate
Thanks. I was learning Hamiltonian Mechanics (I'm asked to find Hamilton's equations after this part) a few months after I took my classical mechanics class which covered lagrangians but not hamiltonians. So I forgot the standard coordinates that are used in a two-body problem. Thanks.