Quantum physics question

[DarkAntimatter]

4 hours ago, vlaiv said:

Although those concepts are related to math, understanding them is related to physics more - why those particular mathematical constructs are used when they are used.

Out of larger class of mathematical constructs, each having certain features, these are used in physics because of their suitability - they fit underlying physics.

Maybe this analogy will help - consider vectors - little arrow ones. We have vectors in 2d, 3d and higher dimensions. Once you understand basic concepts related to them - like their addition, dot product and so on - you have mathematical knowledge of vectors, but calculating mechanical system in 3d requires 3d vectors - particular kind of vectors and you need to know what sort of mathematical manipulations yield physical results - that is related to physics rather than mathematics.

So better to learn these directly and why they are needed I suppose.  

[vlaiv]

4 hours ago, andrew s said:

One thing I find fascinating is that classical physics uses the simplest probability a + b + c ... =1 where  a,b,c.. are the individual probabilities of the individual possible outcomes and QM has a^2 + b^2 + c^2 ... = 1 i.e. the next  most complex "generalised" probability where a^2,b^2,c^2... are the probabilities of the individual  possible outcomes and the a,b,c... the possible states.

I know, a somewhat geeky fascination.

Regards Andrew

 

I've got one as well - what if complex plain is not "complex" at all - but just a two component vector that has addition and other operations defined in a slightly different way. Thinking in complex numbers produces that sort of feeling - and it's not proper number at all - it contains imaginary part!

[andrew s]

10 minutes ago, vlaiv said:

I've got one as well - what if complex plain is not "complex" at all - but just a two component vector that has addition and other operations defined in a slightly different way. Thinking in complex numbers produces that sort of feeling - and it's not proper number at all - it contains imaginary part!

I had similar thoughts but you can have multi component vectors who's members are real or complex. In addition we have quaternions which generalise complex numbers.  However, as an algebra with specific operations then I can't argue with that as they are isomorphic. 

Regards Andrew 

[DarkAntimatter]

2 hours ago, andrew s said:

I had similar thoughts but you can have multi component vectors who's members are real or complex. In addition we have quaternions which generalise complex numbers.  However, as an algebra with specific operations then I can't argue with that as they are isomorphic. 

Regards Andrew 

A mathematician would say the complex numbers are just ordered pairs, with a slightly different definition of multiplication.  So I don't see any problem thinking of them as two component vectors.  But with a natural pairing between the "real" and "imaginary" parts.

I find it fascinating that there are reals, then complex, quaternions, and octonians, but  those are all the division algebras over the field of reals; there are none made of 3 or 7 or 10 or whatever.

[Nigella Bryant]

You lot have lost me completely with all the above, wooosh, over my head, lol.

[Space Oddities]

On 07/08/2019 at 11:00, Nigella Bryant said:

Hi all, is there an idiots guide to quantum physics? 

I found the videos of Professor Dave on Youtube extremely well made and informative. There's a playlist for general physics, which includes the various quantum theories (the available videos are visible on the right side).

Each video is about 5 to 15 minutes long, and contains plenty of drawings, examples and sometimes exercises. It's a good way to understand the key concepts of these complex topics, and I find the videos very accessible for beginners.

The Astronomy playlist is also very nice, it helped me understand how our universe works. I particularly like his video debunking Flat Earth with has a very scientific approach.

[choochoo_baloo]

On 09/08/2019 at 04:52, DarkAntimatter said:

Out of curiosity, which maths do you recommend in order to have a good understanding of QM?

I would strongly suggest reading through an A Level Pure maths book, to get a decent grasp of both

calculus (mainly differentiation).

complex numbers (in short why we have to create another layer of maths above "real" numbers to deal with sqrt(-1)... to then read first few chapters of "Introduction to Quantum Mechanics" by David Griffiths, 2nd Ed. This book is oustanding - it made second year quantum mechanics actually enjoyable...!

 

My summary of QM: classical mechanics can describe any speed/weight/size car driving around a bend. Whereas when zooing into the atomic level, "Quantum mechanics" dictates that the scaled down car can only exist in certain lanes of said bend, travelling at correspodingly discrete speeds. "Quantum" literally means quantised mechanics (think UK shoe sizes; there is no size 10.368247586 shoe, only discrete values).

Only quantum mechanics can explain why an electron can exist in stable atoms, by possessing quantised amounts of energye. Also how semiconductors behave - why certain dopants added to silicon make a CCD camera more sensitive for a certain wavelength.

This stuff is counter-inutitive with our macroscopic pre-conceptions... and I believe this gives it is this (undeserved) mysterious reputation.

Be persistent, this stuff is 'hard' for a reason, and interest is the only prerequisite!

Edited August 12, 2019 by choochoo_baloo
Lots of typo's...