Name: A modern approach to quantum mechanics
ISBN: 9780070651197

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jwuphysicsOct 2022

Nice book, I really like this approach. I also think Townsend's A Modern Approach to Quantum Mechanics is a wonderful book. It's similar to Sakurai but a bit more intelligible for undergrads.

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SteuardAug 2018

I should probably write this up more formally somewhere. But have a look, and it would be cool if you'd give me credit somewhere if you use these notes in your own stuff (I'm Steuard Jensen, and I'm a professor at Alma College). For each course below, the books are listed in roughly my order of preference. This is far, far from being every book for each course or even every popular one, but it's a start.

Intro Physics (Mechanics, E&M, waves, etc.):

* Six Ideas That Shaped Physics, by Tom Moore: Conservation laws first, and a nice conceptual approach (and can incorporate "modern physics" along the way).

* Matter and Interactions, by Chabay and Sherwood: Integrated VPython programming, and uses "true" relativistic mechanics right from the start (and quantum's built in, too).

* Physics for Scientists and Engineers, by Randall Knight: As close to a "traditional" intro book as you can get while still paying attention to physics education research. It's very good, though I feel like the latest edition has veered back a bit to a bit more traditional order, perhaps to make it smoother for old professors to switch.

Uncertanity/Error Analysis: (Essential for understanding experimental physics)

* An Introduction to Error Analysis, by John Taylor: Such a beautiful little book!

"Modern Physics": (Is a class whose content mostly ends before 1950 really "modern"?)

* Six Ideas That Shaped Physics (Units R and Q), by Tom Moore: A very nice first introduction to both special relativity and quantum physics. Might need some supplemental content if you have time for more advanced quantum/nuclear stuff.

[* Special Relativity, by Tom Helliwell: I learned out of this, and it was very good. I haven't taught out of it.]

[* Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, by Eisberg and Resnick: I learned out of this, but haven't taught out of it. Comprehensive.]

Intermediate Classical Dynamics: (I haven't taught this one!)

* ?Classical Mechanics, by John Taylor: I've heard very good things about this one.

[* Classical Dynamics of Particles and Systems, by Thornton and Marion: I learned out of it. It was fine.]

Intermediate Electromagnetism:

* Introduction to Electrodynamics, by David Griffiths: Truly excellent introduction to analysis of electric and magnetic fields using vector calculus and partial differential equations.

[* ?Classical Electromagnetic Radiation, by Heald and Marion: I learned out of this. Not my favorite book, but it did the job.]

Intermediate Quantum Mechanics:

* A Modern Approach to Quantum Mechanics, by John Townsend: Inspired by Sakurai's graduate text, Townsend starts by studying spin and Stern-Gerlach experiments in depth using Dirac bra-ket notation, and then progresses to time evolution and position space. The chapter on the path integral formulation is fun but optional, and there's good stuff on perturbation theory and scattering and some hints toward field theory. (This may work best if students had a strong "Modern Physics" course first that studied wavefunctions in some depth.)

[* Introduction to Quantum Mechanics, by David Griffiths: I haven't used this myself. An excellent quantum book with a more "traditional" organization, starting with wavefunctions and only later talking about Dirac notation and spin.]

Thermodynamics and Statistical Mechanics:

* An Introduction to Thermal Physics, by Daniel Schroeder: A fantastic, multi-pass blend of statistical mechanics and classical thermodynamics. It starts with basic classical definitions of thermal concepts, then introduces explicit state counting in medium-sized systems with the help of Excel, then discusses classical thermodynamics in depth, and finally goes into a full discussion Boltzmann factors and statmech.

* Fundamentals of Statistical and Thermal Physics, by Frederick Reif: This was (for me) the least bad of the books that I used to teach myself undergraduate statmech while I was in graduate school. (I foolishly arranged to avoid the class as an undergrad.)

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jacobolusMar 2010

The infinite injury article is (IMO) complete hogwash. Its author assumes (but never explores or explains the assumption) that there's some unidirectional arrow of improved understanding and pedagogy through time (“progress”) and that therefore modern explanations are inherently more sophisticated/subtle/polished than the original grapplings with a subject.

What he misses is that the seminal papers in any field are forced to really grapple with a subject for its own sake, while later works fetishize dogma and ceaselessly pander to the interests of whoever is paying for the work to be done, simplifying concepts to be understood by those of uncertain prior experience, and packing in features (ooh, glossy pictures! companion website!) that will sell copies.

There are some areas where studying the originals is not especially helpful, because subjects weren’t yet understood. For instance, the founders of quantum mechanics really had no clue what was going on at the beginning, and their early papers are mishmashes of math pulled from other sources which sometimes fortuitously explained their experimental results. So by all means, go grab Townsend’s Modern Approach to Quantum Mechanics (2002) as a more practical and informative work.

In other areas, the famous “originals” (which is to say, those works which were good enough to last centuries while their contemporaries faded into oblivion) are wonderful. There’s much more insight packed into Machiavelli, Tocqueville, or James Madison’s writing than any modern political science textbooks.

And yes, economics as a field would be way better off if its practitioners had any idea what its foundational assumptions were about, or tried really deeply considering (e.g.) Smith, Veblen, Marx, or Keynes (or even, say, Von Neumann and Morgenstern), who had a real world to answer to, not just other economists.

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chronalApr 2020

For context I studied physics for about 2 years in university, before I switched to maths with the intention of returning with better mathematical foundations.

That being said let's start with the maths you will need to be comfortable with:

- Complex Numbers (e^(i*theta))

- Linear Algebra (Matrix Multiplication, Basis of a vector space, Finding Eigenvalues)

- Calculus and some Differential Equations (Taylor Expansions, Solving DEs)

- Probability, Expectation values and Distributions

That's probably what you'll need to dive into textbooks. For a deeper understanding, it would help to know these (worry about these later):

- Analysis (My math major friends say that functional analysis is required later on)

- Hamiltonian Mechanics (QM is littered with Hamiltonians)

- Group theory (if you want to get into Particle Physics)

I'd also recommend having a good grasp on classical mechanics because quantum mechanics builds on it. On my todo list is to review this using:

- The Feynman Lectures on Physics, Volume I available at https://feynmanlectures.caltech.edu/I_toc.html

- Structure and Interpretation of Classical Mechanics by Sussman and Wisdom available at https://mitpress-request.mit.edu/sites/default/files/titles/...

As for books, at uni we used:

- Quantum Mechanics by McIntyre, Manogue and Tate during 2nd year

- A Modern Approach to Quantum Mechanics by Townsend during 3rd year

They generally do a good job covering the material and explain things well.

As for other resources, I haven't read these but they are generally recommended:

- Introduction to Quantum Mechanics by David Griffiths (I liked the author's writing style in his EM book)

- The Feynman Lectures on Physics, Volume III available at https://feynmanlectures.caltech.edu/III_toc.html

- Quantum Computing Since Democritus by Scott Aaronson (I was recommended this for understanding why complex numbers are used in QM)

Some other miscellaneous resources:

- http://www.staff.science.uu.nl/~gadda001/goodtheorist/primar...

- https://www.youtube.com/3blue1brown (The essence of Linear Algebra series is excellent)

- https://ocw.mit.edu/index.htm (In case you want to watch lectures)

- https://physicstravelguide.com/

All of this is at an undergraduate level. It's probably best to grab one of the books and start running through, consulting the others when you want another explanation.

Let me know if you have any further questions. QM is damn cool dude, I hope you have a fun time delving into it.

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