7 ms·

Quantum Mechanics, Concise Book

83 points by pykello 1y ago

hodgehog11 1y ago
Nice, I like how you start out with the finite dimensional case here. Personally though, I don't think I really "got" quantum mechanics until I saw Bell's inequality, so I prefer to put that front and center. Maybe a pointless nitpick, but is a PDF on GitHub really the best way to distribute this though? I guess you also didn't want to give away the .tex file? arXiv is usually the best place to upload these kinds of notes so they can be indexed and easily found.
- paulpauper 1y ago
  As I understand it, arXiv is for research-level original work , not for uploading textbooks or notes.
non_aligned 1y ago
This is fantastic, although the statement about the intended audience cracked me up a bit: "intended for a general audience including ... anyone interested in a concise intro/overview of QM. Prerequisites: linear algebra, calculus, ..." The PDF is essentially higher math with QM-related narrative interspersed here and there. Even if you're a STEM graduate, I found that these skills atrophy pretty quickly if you're not using them day-to-day in your work. Scientists often vastly overestimate how conversant their readers are with "obvious" prerequisites such as vector calculus. And you can often tell on HN, because you have a thread where two mathematicians chat with each other, and then everyone else is just relating anecdotes about quantum mechanics.
- horn1ot 1y ago
  It's like when the doctor says "this won't hurt at all". It WILL hurt your brain, QM is not easy. I'm looking for a QM book structured similar to Norvig LISP books, ie following a demonstrative didactic method, by building computational implementations of toy models demonstrating various aspects of QM (not just QC), toy models of resonator, particle in a box, etc
  - ziofill 1y ago
    I’ve been writing something like that for a bit, not ready yet but there’s hope! ^^
    - horn1ot 1y ago
      I'd be very interested to read that, as would many others here I'm sure. Care to share a few chapters on your GitHub?
      - ziofill 1y ago
        It’s still not too early, but I will
pkoird 1y ago
Nice effort. As far as textbooks for QM, Electrodynamics, and any sufficiently complex field of study goes, I always feel that these have been written using abstractions that people have developed much later retroactively. I understand the advantages: it makes the entire content concise, structured, and basically straightforward. However, what I crave is a technical book that is based upon the history of the subject. Something that doesn't start immediately with Hilbert spaces but starts off by talking about why Max Plank did what he did, how did Einstein improve upon it, what mistakes were made, what misguided hypothesis were later corrected in what manner, how were different things then unified... you get the point. I think this narrative based approach would motivate me much better than something that's condensed and distilled.
- LordGrignard 1y ago
  I think the book called "Quantum mechanics" by max Planck and Neil bohr is quite similar to what you need. And atleast in my country it's available for less than 2.5$ usd converted so it's pretty damn cheap However of course I think you'd be able to find an ebook about it too Just include max Planck and neil bohr as the authors lol.
- abdullahkhalids 1y ago
  Most Physics undergraduate programs have a course on Modern Physics, which is often taught in the way you are asking for. Though only up to the origins of quantum mechanics. This textbook, for example does this [1]. The problem is that after the basics of QM, there were literally hundreds of papers by dozens of important scientists developing the subsequent theory. And you can no longer teach the subject in a linear historical fashion. [1] https://www.cengage.com/c/modern-physics-3e-serway-moses-moyer/9780534493394/ https://www.cengage.com/c/modern-physics-3e-serway-moses-moy...
- chamomeal 1y ago
  The book “quantum” was a great read. Doesn’t really delve into any theories, but covers the general story of the physicists on the eve of QM
  - 1y ago
mieses 1y ago
As a member of the general audience I was disappointed to find no color illustrations. Faced with walls of text and an absence of enjoyable distraction and marginalia, I began to think (which rarely happens) "wouldn't the relevant audience desire more mathematical equations?". And then I closed the pdf.
sesm 1y ago
One issue: 'classical mechanics' section doesn't introduce Hamiltonian, and instead it's introduced in chapter 2.2 as if it is a QM concept. In my uni Classical Mechanics course was a pre-requisite to QM to ensure that students have a good intuition about Lagrangian and Hamiltonian formalisms, because those are non-trivial concepts by themselves.
- adrian_b 1y ago
  Off topic, but the utility of the Hamiltonian is debatable. You can solve any problem by using only the Lagrangian, there is really no need for the Hamiltonian, which also has the disadvantage of not being relativistically invariant, like the Lagrangian. Also the name of "Hamiltonian" is somewhat misused. The most important contribution of Hamilton has been the definition of Hamilton's integral, i.e. the integral over time of the Lagrangian. That is an extremely important function and it would have deserved better the name of "Hamiltonian", than the less important Hamiltonian, which also was not introduced for the first time by Hamilton. How to transform the system of equations of Lagrange to the "Hamiltonian" form had already been described by Poisson, and then by Cauchy, the latter using a form exactly equivalent to that presented later by Hamilton. The notation H for the Hamiltonian has nothing to do with the name of Hamilton. Lagrange had used H for this quantity in 1811, without giving any meaning to the letter, then Hamilton in 1834 has reused the notations of Lagrange, adding "function S" for Hamilton's integral, also without giving any meanings to the letters.
FilosofumRex 1y ago
It's wrong to assume people know classical physics formalism well and then and only then, they'll learn QM! QM pedagogy problem is, how to teach QM to people who don't know physics beyond [F= ma], and math beyond algebra, differential calculus, & virtually no probability beyond mean & std dev?
- hershkumar 1y ago
  Practically speaking, QM can be taught without the assumption that students understand the Hamiltonian formalism, simply by starting with Hilbert spaces and operators on Hilbert spaces. In fact, I would claim that having taken a class on basic linear algebra would better prepare you to understand quantum mechanics than mastering classical mechanics. QM is generally taught by referencing classical mechanics, but I believe that's more reflective of the fact that most universities require classical mechanics as a core course, and students coming in to QM will have generally taken it.
graemep 1y ago
A very short book is Quantum Theory: A Very Short Introduction, part of Oxford University Press's very short introduction series is good.
hyperman1 1y ago
After a colleague asked about this, my interest was primed on quantum computing. I found wikipedia hard to follow and the textbooks were really expensive. Then I stumbled on this course by IBM: https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/single-systems/classical-information https://quantum.cloud.ibm.com/learning/en/courses/basics-of-... It has prereqs in complex numbers and linear algebra, but is quite easy to follow if you have these. I like how it first uses quantum notations to describe the non quantum world, so you get used to the reasoning. Then it adds the actual quantum stuff on top of the now understandable reasoning.
stared 1y ago
Note sure if it is the route I recommend. Starting with classical mechanics takes more background that needed, is likely to be more confusing that needed and to build very wrong intuitions and conceptions. I really suggest starting with quantum itself, before spin-1/2 systems are easier to start, and photons (in my opinion), even easier (vide Sec. 2 in https://doi.org/10.1117/1.OE.61.8.081809 https://doi.org/10.1117/1.OE.61.8.081809). So, I recommend starting from "Quantum Mechanics Theoretical Minimum" by Leonard Susskind and Art Friedman, "Six Quantum Pieces: A First Course in Quantum Physics" by Valerio Scarani or "Introduction to Quantum Information Science" by Artur Ekert (https://github.com/thosgood/qubit.guide https://github.com/thosgood/qubit.guide). To dive deeper, I recommend " Lectures on Quantum Mechanics" by Berthold-Georg Englert.

83 points by pykello 1y ago

Nice, I like how you start out with the finite dimensional case here. Personally though, I don't think I really "got" quantum mechanics until I saw Bell's inequality, so I prefer to put that front and center. Maybe a pointless nitpick, but is a PDF on GitHub really the best way to distribute this though? I guess you also didn't want to give away the .tex file? arXiv is usually the best place to upload these kinds of notes so they can be indexed and easily found.

paulpauper 1y ago
As I understand it, arXiv is for research-level original work , not for uploading textbooks or notes.

non_aligned 1y ago

This is fantastic, although the statement about the intended audience cracked me up a bit: "intended for a general audience including ... anyone interested in a concise intro/overview of QM. Prerequisites: linear algebra, calculus, ..." The PDF is essentially higher math with QM-related narrative interspersed here and there. Even if you're a STEM graduate, I found that these skills atrophy pretty quickly if you're not using them day-to-day in your work. Scientists often vastly overestimate how conversant their readers are with "obvious" prerequisites such as vector calculus. And you can often tell on HN, because you have a thread where two mathematicians chat with each other, and then everyone else is just relating anecdotes about quantum mechanics.

horn1ot 1y ago
It's like when the doctor says "this won't hurt at all". It WILL hurt your brain, QM is not easy. I'm looking for a QM book structured similar to Norvig LISP books, ie following a demonstrative didactic method, by building computational implementations of toy models demonstrating various aspects of QM (not just QC), toy models of resonator, particle in a box, etc
- ziofill 1y ago
  I’ve been writing something like that for a bit, not ready yet but there’s hope! ^^
  - horn1ot 1y ago
    I'd be very interested to read that, as would many others here I'm sure. Care to share a few chapters on your GitHub?
    - ziofill 1y ago
      It’s still not too early, but I will

pkoird 1y ago

Nice effort. As far as textbooks for QM, Electrodynamics, and any sufficiently complex field of study goes, I always feel that these have been written using abstractions that people have developed much later retroactively. I understand the advantages: it makes the entire content concise, structured, and basically straightforward. However, what I crave is a technical book that is based upon the history of the subject. Something that doesn't start immediately with Hilbert spaces but starts off by talking about why Max Plank did what he did, how did Einstein improve upon it, what mistakes were made, what misguided hypothesis were later corrected in what manner, how were different things then unified... you get the point. I think this narrative based approach would motivate me much better than something that's condensed and distilled.

LordGrignard 1y ago
I think the book called "Quantum mechanics" by max Planck and Neil bohr is quite similar to what you need. And atleast in my country it's available for less than 2.5$ usd converted so it's pretty damn cheap However of course I think you'd be able to find an ebook about it too Just include max Planck and neil bohr as the authors lol.
abdullahkhalids 1y ago
Most Physics undergraduate programs have a course on Modern Physics, which is often taught in the way you are asking for. Though only up to the origins of quantum mechanics. This textbook, for example does this [1]. The problem is that after the basics of QM, there were literally hundreds of papers by dozens of important scientists developing the subsequent theory. And you can no longer teach the subject in a linear historical fashion. [1] https://www.cengage.com/c/modern-physics-3e-serway-moses-moyer/9780534493394/ https://www.cengage.com/c/modern-physics-3e-serway-moses-moy...
chamomeal 1y ago
The book “quantum” was a great read. Doesn’t really delve into any theories, but covers the general story of the physicists on the eve of QM
- 1y ago

mieses 1y ago

As a member of the general audience I was disappointed to find no color illustrations. Faced with walls of text and an absence of enjoyable distraction and marginalia, I began to think (which rarely happens) "wouldn't the relevant audience desire more mathematical equations?". And then I closed the pdf.

sesm 1y ago

One issue: 'classical mechanics' section doesn't introduce Hamiltonian, and instead it's introduced in chapter 2.2 as if it is a QM concept. In my uni Classical Mechanics course was a pre-requisite to QM to ensure that students have a good intuition about Lagrangian and Hamiltonian formalisms, because those are non-trivial concepts by themselves.

adrian_b 1y ago
Off topic, but the utility of the Hamiltonian is debatable. You can solve any problem by using only the Lagrangian, there is really no need for the Hamiltonian, which also has the disadvantage of not being relativistically invariant, like the Lagrangian. Also the name of "Hamiltonian" is somewhat misused. The most important contribution of Hamilton has been the definition of Hamilton's integral, i.e. the integral over time of the Lagrangian. That is an extremely important function and it would have deserved better the name of "Hamiltonian", than the less important Hamiltonian, which also was not introduced for the first time by Hamilton. How to transform the system of equations of Lagrange to the "Hamiltonian" form had already been described by Poisson, and then by Cauchy, the latter using a form exactly equivalent to that presented later by Hamilton. The notation H for the Hamiltonian has nothing to do with the name of Hamilton. Lagrange had used H for this quantity in 1811, without giving any meaning to the letter, then Hamilton in 1834 has reused the notations of Lagrange, adding "function S" for Hamilton's integral, also without giving any meanings to the letters.

FilosofumRex 1y ago

It's wrong to assume people know classical physics formalism well and then and only then, they'll learn QM! QM pedagogy problem is, how to teach QM to people who don't know physics beyond [F= ma], and math beyond algebra, differential calculus, & virtually no probability beyond mean & std dev?

hershkumar 1y ago
Practically speaking, QM can be taught without the assumption that students understand the Hamiltonian formalism, simply by starting with Hilbert spaces and operators on Hilbert spaces. In fact, I would claim that having taken a class on basic linear algebra would better prepare you to understand quantum mechanics than mastering classical mechanics. QM is generally taught by referencing classical mechanics, but I believe that's more reflective of the fact that most universities require classical mechanics as a core course, and students coming in to QM will have generally taken it.

graemep 1y ago

A very short book is Quantum Theory: A Very Short Introduction, part of Oxford University Press's very short introduction series is good.

hyperman1 1y ago

After a colleague asked about this, my interest was primed on quantum computing. I found wikipedia hard to follow and the textbooks were really expensive. Then I stumbled on this course by IBM: https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/single-systems/classical-information https://quantum.cloud.ibm.com/learning/en/courses/basics-of-... It has prereqs in complex numbers and linear algebra, but is quite easy to follow if you have these. I like how it first uses quantum notations to describe the non quantum world, so you get used to the reasoning. Then it adds the actual quantum stuff on top of the now understandable reasoning.

stared 1y ago

Note sure if it is the route I recommend. Starting with classical mechanics takes more background that needed, is likely to be more confusing that needed and to build very wrong intuitions and conceptions. I really suggest starting with quantum itself, before spin-1/2 systems are easier to start, and photons (in my opinion), even easier (vide Sec. 2 in https://doi.org/10.1117/1.OE.61.8.081809 https://doi.org/10.1117/1.OE.61.8.081809). So, I recommend starting from "Quantum Mechanics Theoretical Minimum" by Leonard Susskind and Art Friedman, "Six Quantum Pieces: A First Course in Quantum Physics" by Valerio Scarani or "Introduction to Quantum Information Science" by Artur Ekert (https://github.com/thosgood/qubit.guide https://github.com/thosgood/qubit.guide). To dive deeper, I recommend " Lectures on Quantum Mechanics" by Berthold-Georg Englert.