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March 10

Good Classical Physics Book For A Math Person

I have always been fascinated by physics, but I have a terrible time of learning it - not the mathematics parts, but the way that physics books use mathematics and the physical assumptions that inform on that (which are often unstated). Indeed, I am in a weird position in that I study mathematics and, actually, have an easier time with physics the more removed it gets from day to day life (where things have to be laid out more carefully and clearly for the reader). However, so while I can make my way through a book on quantum physics, on math alone, and skim through the parts that draw directly from classical mechanics, I can't go much beyond this because I don't have a good foundation for the subject. So, does anyone know of any good books on classical mechanics (especially those that get into classical field theory at some point) that are written with math majors in mind? It would be doubly awesome if the book did help develop physical intuition, or an intuition for these subjects as held by physicists. I am not asking for a book that develops the mathematics of classical mechanics, by itself, that isn't especially difficult for me, but for a book that could hold my hand, so to speak, with the physics side of it (and, if possible, doesn't use math tricks without explaining them - even in simple cases where the math clearly works out, several of the books of read seem to just assert results more on the basis that that should be the case than because of any mathematical justification, which makes even basic math feel slippery when paired up with physics to me). **For a specific example, the last such book I tried reading was discussing unit vectors in spherical and cylindrical coordinates, which isn't a difficult concept, but they immediately began to use them without any clarification on why they could use them that way, it was very hand wavy - after sitting down and writing it out a little, it wasn't difficult to follow. The problem here, for me, wasn't that I need to get more comfortable with the math and they were just assuming I was, but that there were physical assumptions about what we were doing that were being used to handwave why you can do this and that; indeed, I would have been more comfortable with skipping steps in a mathematical concept than appeals to why you can treat the dot product a certain way because of work and force. In short, I would love a book that reads more like a math book and builds up from first principles, as much as possible, while explaining the physics that follows from there, rather than the opposite way around. Thank you for any help to this rather ranty and rambling request:-)24.3.61.185 (talk) 10:55, 10 March 2018 (UTC)[reply]

Other readers may have the same problem. I found that Mathematics for the Million: How to Master the Magic of Numbers illuminated the whole landscape and help me to become aware of what laid in the shadows of my current knowledge. As for The Dancing Wu Li Masters it is a must, because it is such a good read, even if one is not interested in either physics nor mathematics. --Aspro (talk) 13:28, 10 March 2018 (UTC)[reply]

Have you tried The Feynman Lectures on Physics? --catslash (talk) 14:08, 10 March 2018 (UTC)[reply]

The guy doesn't seem to have trouble with mathematics, but rather with classical physics. Feynman's lectures volumes (I & II) isn't a good idea from another aspect - it isn't a conventional textbook and aims towards somewhat more advanced. I'd recommend Physics, by Halliday & Resnick, or Principles of Physics, by Walker, Halliday & Resnick, or even Sears & Zemansky book. All three suggestions suit your needs, as I see them. Enjoy & good luck. בנצי (talk) 18:37, 10 March 2018 (UTC)[reply]

I tutored a smart 14 year old using Feynman's lectures as the main resource, because I like Feynman's approach. Greglocock (talk) 20:08, 10 March 2018 (UTC)[reply]

We have articles on those books: Fundamentals of Physics and, University Physics. Rereading the OP's question, I now see that the area of interest is classical mechanics rather than classical physics in general - in which case Feynman would not be suitable. For general physics, Feynmam is strong on physical intuition though. --catslash (talk) 20:25, 10 March 2018 (UTC)[reply]

You might look at the Manchester Physics Series --Phil Holmes (talk) 10:52, 11 March 2018 (UTC)[reply]

Feynman's lectures is a textbook in conceptual physics. However, from my point of view, when you are focusing on the ideas rather than on the math, it is even more difficult to understand physics (which is, basically, a mathematical explanation of the real world). In Feynman's lectures, the math ideas are just mentioned. Or not even that. Sometimes, you are supposed to match a physical explanation to the math fundamentals. That's hardly a good practice in textbook writing, since it would alienate many non-advanced learners.

And what's more important, it won't help you solve neither real problems nor constructed problems as exercises. I'd use it only as a complement, and that after getting a good basis from textbooks like Halliday's or Young, Freedman, and Ford's or Wolfson, Richard and Jay Pasachoff's.Doroletho (talk) 12:28, 11 March 2018 (UTC)[reply]

The books in Leonard Susskind's The Theoretical Minimum series start from first principles, and are accompanied by video lectures available on YouTube. Part 1 focuses on classical mechanics, and Part 3 covers classical field theory. Gandalf61 (talk) 13:01, 12 March 2018 (UTC)[reply]

One of his colleagues has just reminded me of this; Vincent Icke (1995). The Force of Symmetry. which is excellently readable as an intro to quantum behaviour; relativity; and symmetry. Andy Dingley (talk) 13:55, 14 March 2018 (UTC)[reply]

Regarding spectroscopy of Hg vapors

One of the spectral lines emitted by Hg gas is the strong 253.7 nm line, known well experimentally. The transition responsible for this line is from ³P₁ triple state to ¹S₀ singlet state. However, it seems that I'm missing something here: since the 1st state is of multiplicity=3, meaning 2S+1=3 >> S=1, and given J=1, we get l=0, contrary to having P state, which is l=1 ! - What have I missed here ?
Why, for a given atom (with 2 outer electrons), singlet states are higher in energy in comparison to the triplet states (e.g., parahelium (singlet states) to orthohelium (triplet states) upon collisions) ? If not always so, when they are, and when they aren't ?
And, related to the previous question: are there transitions from triplets to (lower) singlets ? I don't see why not, but judging from a quite detailed energy-level of Hg vapors diagram (discussed in a textbook) I'm reviewing no such transitions could be seen. Thank you for any light shed on these issues, בנצי (talk) 19:05, 10 March 2018 (UTC)[reply]
- You should read Angular_momentum_coupling. Coupling spin 1 and orbital momentum 1 may result in the total angular momentum being 0,1 or 2.
- I am not sure that understand your question? In the your own example it is not the case.
- I do not understand either.

Ruslik_Zero 20:33, 10 March 2018 (UTC)[reply]

Thank you. Without reading more than what you recommend, my question couldn't be phrased the way it was. Anyway, I'm missing something, and I've to look up what you indicate in your answer.
I'll put it more simply, using Helium example I mentioned: why the triplet state of He is lower in energy than the singlet state ? Let's start with.

If you mean why ³S₁ state is lower in energy than ¹S₀ state? It is explained by exchange energy. Ruslik_Zero 08:00, 11 March 2018 (UTC)[reply]

If you examine any energy-level diagram of Hg, you'll see many transitions, but all of them from triplet states to singlets. I can send a picture of such a diagram, taken from the textbook I'm using, but I'm not sure it's permitted (edited in 1987). However, I can send it to you privately, if you allow me. Furthermore, in He the opposite is true - collisions cause excited He atoms (orthohelium) lose energy and become parahelium, while the opposite is true for paraheliums. I hope my last 2 question are clearer now. בנצי (talk) 21:53, 10 March 2018 (UTC)[reply]

Can you elaborate on your answer to the 1st question ? It's the 1st term symbol I've cited before that I don't understand, as detailed before. בנצי (talk) 23:11, 10 March 2018 (UTC)[reply]

You do not understand how angular momentums are coupled in the quantum mechanics. You can read the article I cited above or (better) a text book. Ruslik_Zero 08:00, 11 March 2018 (UTC)[reply]

Well, I'm not participating in a quiz. If you want to answer the point in question, please do, and don't keep sending me to a textbook or alike, ignoring the fact that I did so. Regular people don't raise questions without trying the usual ways before. Regular people also don't just 'give grades' without the slightest effort to help. You can't just deny efforts done. For sure I'm stuck in an unclear point. If you don't want to be clearer on this, fine, leave this discussion to more patient colleages. Thank you, בנצי (talk) 11:37, 11 March 2018 (UTC)[reply]

Coupling angular moments is such a basic concept in the quantum mechanics that, if you are seriously studying theoretical physics, you must understand it before you can go any further. However this forum is not a right place to learn how to do this correctly. There is simply no space and no time to do this here. You should address your questions to your teachers and text books. Ruslik_Zero 15:52, 11 March 2018 (UTC)[reply]

The last point is that these may be forbidden transitions, and require emission via less likely magnetic dipole, or, electric quadrupole mechanisms. So often the lowest triplet state is metastable and long lasting. It may then be destroyed by collisions with other atoms rather than losing photons. Graeme Bartlett (talk) 21:40, 10 March 2018 (UTC)[reply]

I've to consider your point here, including its relevance to the subject in question. Thank you, בנצי (talk) 21:53, 10 March 2018 (UTC)[reply]

You are proposing some triplet to singlet transitions that are not observed in the spectrum. The relevance is that if these transitions existed they would be forbidden transitions. The transition cannot happen by the normal electric dipole change which emits a photon. Instead they can only happen by those other rarer mechanisms. Because the emission by these mechanisms is unlikely, it takes a long time before it happens. So long in fact that the atom instead bumps into something else first and then undergoes a more complex energy loss, without emitting that photon. Graeme Bartlett (talk) 00:43, 11 March 2018 (UTC)[reply]

I think hyperphysics [1] gives a more approachable explanation in some ways of orthohelium than our article - mostly because we don't have a separate article for orthohelium and parahelium. The key thing is that although spin is often treated like some totally abstract thing about an electron, yet, two electrons in two helium orbitals with parallel spins manage to stay further apart than those with antiparallel spins. I would love to see some resources further explaining what that looks like (in simulation) and explaining how it is/what it means that up + down get remixed into parallel and antiparallel. I think quantum mechanics should be intuitively comprehensible, but too many people just treat it as mathematical rote. Wnt (talk) 16:13, 11 March 2018 (UTC)[reply]

Orthohelium etc isn't the main issue I'm concerned with. By the way, how do you make a search in HyperPhysics ? I didn't see any 'search box' there.

I'm mainly concerned right now, with 2 issues: (a) understanding ³P₁, as described before in this discussion; & (b) how the way angular momenta are added to get J, depending on whether spin-orbit interaction is concerned or jj coupling. In other words, how the relative strength of relevant interactions dictate one order of vector addition or another. בנצי (talk) 20:07, 11 March 2018 (UTC)[reply]