How to get started with quantum mechanics?

[firipu1]

Hi users,
by the past few months I've gotten really interested in space / quantum mechanics things. I had even read book written by Stephen Hawking 'History of time' which was really interesting but hard to understand as well. So the point it - I want to understand the Rules of Quantum Mechanics better but I don't know how to get started. What issues should I learn first, before taking challenge with quants?
Sorry if I've made mistakes and hope you will help me. Thanks :)

 

[lugita15]

To get a general, nonmathematical idea of how quantum mechanics works, I suggest you read the short book "QED: the strange theory of light and matter" by Richard Feynman. Once you read that, then you can read more mathematically precise texts.

 

[DevilsAvocado]

Welcome to PF firipu1!

Richard Feynman is of course brilliant. If you prefer the original the Sir Douglas Robb lectures at the University of Auckland (1979), it’s available on YouTube:

QED: The Strange Theory of Light and Matter
https://www.youtube.com/watch?v=LPDP_8X5Hug
The playlist consist of 30 videos between 10-15 min (from the original).

Another “QM for Dummies” is Brian Greene’s video on Nova:

Nova - Fabric of the cosmos: Quantum leap - hosted by Brian Greene
https://www.youtube.com/watch?v=qWijXLos8Oo


When it comes to books for beginners I could recommend Quantum Theory: A Very Short Introduction, John Polkinghorne (2002) ~100 pages for 10 bucks on Amazon. It doesn’t require any mathematics but provide the option in appendix. From the preface:

... the enjoyment of quantum ideas should not be the sole preserve of theoretical physicists. Although the full articulation of the theory requires the use of its natural language, mathematics, many of its basic concepts can be made accessible to the general reader who is prepared to take a little trouble in following through a tale of remarkable discovery. This little book is written with such a reader in mind. Its main text does not contain any mathematical equations at all. A short appendix outlines some simple mathematical insights that will give extra illumination to those able to stomach somewhat stronger meat. (Relevant sections of this appendix are cross-referenced in bold type in the main text.)

And of course there’s always Introduction to Quantum Theory - Quantiki wiki and Quantum mechanics - Simple English Wikipedia.

But remember the caveat from Steven Weinberg – After you learn Quantum Mechanics you’re never really the same again!

 

[Jorriss]

Do you want popular science accounts? Or do you want to really learn QM properly in some sense?

 

[lugita15]

Before you look at all these books and videos, maybe you should start with this short video showing how weird quantum mechanics can be:
https://www.youtube.com/watch?v=iVpXrbZ4bnU

 

[DevilsAvocado]

Nah, that cat isn’t particularly weird... teleporting Brian Greene from New York to Paris – that’s weird!

[but I do love the SR-QM-Bell part, nice!]

 

[wotanub]

Start with a "Modern Physics" textbook (Like Rex & Thornton, or the 3rd part of Halliday, Resnick & Walker, extended edition) then move to a Quantum Mechanics book.

 

[MinasKar]

Hmm you can read Introduction to Quantum Mechanics by David J. Griffiths, i think you can easily find it as a pdf file

 

[Ravi Mohan]

I would suggest Feynman lectures Vol III and then, if it amplifies your interest, Modern Quantum Mechanics by J.J Sakurai.

Edit:
I forgot to mention but you can also study Principles of Quantum Mechanics by P.A.M Dirac (besides Sakurai)

 

[NegativeDept]

If you really want to get past pop-sci and heuristic arguments, spend some time learning linear algebra fundamentals. It's essential to know what these words mean:

• vector space
• inner product
• linear combination / superposition
• linear transformation
• orthogonal, normal, orthonormal
• eigenvector, eigenvalue, spectrum
• transpose, adjoint, unitary
• change of basis

Almost every statement about QM with any rigor at all is, unfortunately, soaked in linear algebra jargon. (Example: Possible results of measuring an observable are eigenvalues of the self-adjoint linear operator representing that observable.)

Classical Lagrangian and Hamiltonian mechanics is useful to know, especially because the Hamiltonian operator is a big deal in QM. Some practice with basic probability and statistics is also really valuable.

 

[DevilsAvocado]

I had even read book written by Stephen Hawking 'History of time' which was really interesting but hard to understand as well.

Do you want popular science accounts? Or do you want to really learn QM properly in some sense?

... I think A Brief History of Time includes only a single equation E = mc² ...

What are the odds firipu1 could get a grip on something like this:

(... which by the way scare the hell out of me also ... ;)

I could be wrong; firipu1 might be a mathematical genius (that hasn’t got started yet). But if not – here’s “DevilsAvocado’s Conceptual Crash Course to QM”!

• Step one - Reset your brain.
• For a moment, forget about the ordinary (classical) world where we spend our everyday life, where ‘stuff’ is solid and localized, though it isn’t easy because these things seems hardwired in our brains. When a football player see the ball traveling through the air, he automatically do all these quite complicated calculations to predict where the boll will land a few seconds later, and he runs to catch the ball exactly at the right spot on field. These things happen in the ‘background’ of our brain without any special effort (and this goes for many animals too).
• In QM, ‘stuff’ is not solid and localized, until you try to pin it down (by for example a measurement). Instead you have to think about the microscopic particle in QM as a wave (or wave packet) traveling freely through empty space:
  
  
  
• This QM wave is mathematically described by the Schrödinger equation which is something of the “Holy Grail of QM” and if you going to learn only one of those Greek letters it’s $\Psi$ (pronounced /ˈpsaɪ/) you should know, representing the wavefunction in quantum mechanics.
• The Schrödinger equation, developed by the Austrian physicist Erwin Schrödinger, is not something one solves in kindergarten. To keep it short – it’s weird – and it requires an understanding of complex numbers and partial differential equations. In our everyday life we use real numbers:
  
  
  
• Adding an imaginary number to a real number form a complex number:
  
  
  
• To make it even weirder, the wavefunction doesn’t give any information about the QM particle per se, but only provide the probability for finding the QM particle at a given position:
  
  
  
  
  Left: The real part (blue) and imaginary part (red) of the wavefunction.
  Right: The probability distribution of finding the particle with this wavefunction at a given position.
  The top two rows are examples of stationary states, which correspond to standing waves.
  The bottom row an example of a state which is not a stationary state.
  
  As you see there are ‘imaginary processes’ in the calculation of the wavefunction, to make it possible to get the probabilities of a ‘real output’ in the other end... isn’t that weird!?
  
  There are serious discussion if the wavefunction is real or not (i.e. actually ‘there’), or if it’s just a mathematical abstraction that help us master the quantum world. My recommendation is to treat it as an abstraction until proven otherwise (to sleep well at night ;).
• Finally, the last everyday-life-shock: When we measure ‘the output of the wavefunction’ it always comes in form of on only certain discrete values, quanta. The microscopic QM world is quantized!

Now, you might say – This is false! I’ve seen photos of gold atoms and they look exactly as any other everyday-life-marble!

Sure, it’s true that we can see atoms in modern scanning tunneling microscope, but this is a measurement! We bombard the gold atoms with gazillions of electrons to get this picture, and in the process we disturb the quantum state so much it has to ‘convert’ into the classical state. It’s like the police ‘disturbing’ a demonstration with water cannons to force the demonstrators up against the wall. And furthermore, what we see is not the actual atoms, but the result of ‘electron interactions’.

If you’re lazy like me (and don’t want to spend 10 years on solving the Schrödinger equation ;) you can get a visual hint on what’s going on at the QM level in this java applet/QM simulation, that shows the behavior of a single particle in bound states in one dimension. It solves the Schrödinger equation and allows you to visualize the solutions.

http://www.falstad.com/qm1d/

Good luck with QM!

 

[Ravi Mohan]

@DevilsAvocado
I have to say, you can really make physics spooky.

 

[Jorriss]

... I think A Brief History of Time includes only a single equation E = mc² ...

What are the odds firipu1 could get a grip on something like this:

I don't know, it's why I asked before recommending Sakurai or something.

 

[DevilsAvocado]

@DevilsAvocado
I have to say, you can really make physics spooky.

You aint seen nothing yet... in my final ‘lecture’ I will only talk about Spukhafte Fernwirkung! ()


@Jorriss: No worries mate.

 

[QuantumCurt]

Some of the sources in this thread have been fully invigorating my growing interest in physics. I'm starting physics in the fall...can't wait. I just watched through the first of the Feynman Lectures...incredibly fascinating stuff.

Thanks for posting all of this stuff!

 

[DevilsAvocado]

Good luck with studies QuantumCurt!

 

[QuantumCurt]

Thanks! I've been sifting through all of the material you posted above, and I'm getting more and more interested the deeper into it I'm getting. It's making me even more anxious to get started with physics!

 

[genericusrnme]

assuming you only know high school maths I'd reccomened this course;

Introduction to linear algebra - G. Strang
Basic calculus videos at khan academy
Mathematical Methods in the Physical Sciences - M. Boas
Classical Mechanis - Landau & Lifgarbagez
Non-relitivistic Quantum Mechanics - Landau & Lifgarbagez

I'd stay far away from Griffiths' book on QM, it's one of the worst I've read.
I'd also stay away from Sakurai and Shankar until you've read a little of L&L's book, imo L&L will give you a better feeling for what's going on than Sakurai, Shankar and a lot of other 'modern' QM books.

 

[WannabeNewton]

assuming you only know high school maths I'd reccomened this course;

Introduction to linear algebra - G. Strang
Basic calculus videos at khan academy
Mathematical Methods in the Physical Sciences - M. Boas
Classical Mechanis - Landau & Lifgarbagez
Non-relitivistic Quantum Mechanics - Landau & Lifgarbagez

Is this meant to be a joke?

 

[firipu1]

Sorry I didn't respond for a long time and thank for all threads you put there. Seems like I have to work very hard to understand all of QM.

 

[lugita15]

Sorry I didn't respond for a long time and thank for all threads you put there. Seems like I have to work very hard to understand all of QM.

firipu1, can you tell us what your current level of knowledge is in math and physics? That can help us better tailor the recommendations for you.

 

[firipu1]

Just as 'genericusrnme' mentioned. I'm in high school. But as long as education system in my country is really horrible I'm trying to learn math/physics by my own (or taking some extra lessons from physics).