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I've read Jim Al Khalili and John Gribben's books on the subject. Both are accessible, well written and very informative. Needless to say, after ploughing through these two my undertsanding is still in its usual super positional quantum state of befuddlement :icon_scratch:

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QM is not that complicated at all, what is problematic to most people is math behind it - you need to understand the math in order to understand the QM.

If you have math knowledge, then there is a very good set of lectures online by Leonard Susskind that cover many aspects of physics including much of QM. Lectures are based on his book and titled the same: Theoretical minimum

There is a website with link to videos of lectures on youtube:

https://theoreticalminimum.com/

I find lectures very good although sometimes a bit slower paced than I would like (some concepts are explained multiple times because lectures are recorded in actual class and people have questions, etc ...).

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1 hour ago, vlaiv said:

QM is not that complicated at all, what is problematic to most people is math behind it - you need to understand the math in order to understand the QM.

If you have math knowledge, then there is a very good set of lectures online by Leonard Susskind that cover many aspects of physics including much of QM. Lectures are based on his book and titled the same: Theoretical minimum

There is a website with link to videos of lectures on youtube:

https://theoreticalminimum.com/

I find lectures very good although sometimes a bit slower paced than I would like (some concepts are explained multiple times because lectures are recorded in actual class and people have questions, etc ...).

That content looks interesting.

I just dipped into a couple of lectures. My problem is in having effectively, for the purposes of QM, zero mathematics. I fell behind in junior school on multiplication tables and never caught up! :(

I find it's possible to watch some highly technical lectures and leave the math(s) to wash over my head! Clearly I'm missing some very important detail but the principals usually carry themselves as physical concepts that I can grasp.

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6 hours ago, Nigella Bryant said:

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

At what level do you want the maths pitched? Examples could include, but are not limited to: no maths; elementary rearangement of early high school equations; elementary calculus; more advanced calculus and elementary linear algebra.

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1 minute ago, Nigella Bryant said:

The dumbest the better, lol. I'm pretty much starting from scratch in my 60's. 

"no maths" does not equal "dumb". 🙂

Two of the books mentioned above ('Quantum Mechanics" by Susskind and Friedman, "Quantum Mechanics for Dummies") , do require some maths.

Another interesting book is "the Quantum Universe" by physicists Brian Cox and Jeff Forshaw. This book uses little mathematics, but I wouldn't say that the book is an easy read. Reviewed in The Guardian and the Independent:

https://www.theguardian.com/books/2011/nov/16/quantum-universe-cox-forshaw-review

https://www.independent.co.uk/arts-entertainment/books/reviews/the-quantum-universe-everything-that-can-happen-does-happen-by-brian-cox-and-jeff-forshaw-2374486.html

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2 minutes ago, George Jones said:

"no maths" does not equal "dumb". 🙂

Two of the books mentioned above ('Quantum Mechanics" by Susskind and Friedman, "Quantum Mechanics for Dummies") , do require some maths.

Another interesting book is "the Quantum Universe" by physicists Brian Cox and Jeff Forshaw. This book uses little mathematics, but I wouldn't say that the book is an easy read. Reviewed in The Guardian and the Independent:

https://www.theguardian.com/books/2011/nov/16/quantum-universe-cox-forshaw-review

https://www.independent.co.uk/arts-entertainment/books/reviews/the-quantum-universe-everything-that-can-happen-does-happen-by-brian-cox-and-jeff-forshaw-2374486.html

Many thanks George for your reply. Much appreciated. Been fascinated with it for years. Hopefully I'll understand a little better. 

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Posted (edited)
34 minutes ago, Nigella Bryant said:

Been fascinated with it for years. Hopefully I'll understand a little better. 

If you have questions, there are folks here who have substantial knowledge of quantum theory, but don't expect uniform answers!

Recipe for a pub brawl: 1) take some physicists down the pub; 2) feed them beer for several hours; 3) ask "What does quantum mechanics really mean?".

This is a fun bit of hyperbole, but there is a grain of truth to it. The second edition of the book "Do We Really Understand Quantum Mechanics?" by Franck Laloe was published this year. This book is meant for folks who studied university-level quantum mechanics. Also, the greatest living physicist, Steven Weinberg, in his fairly recent postgrad-level book "Lectures on "Quantum Mechanics" made clear his deep dissatisfaction with the foundations of quantum theory. A huge shock for me!

This type of thing is part of what makes quantum theory so interesting, so I hope that you have some fun.

Edited by George Jones
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As @George Jones implies we know how to crush the number in QM but we have no real understanding as to why it works the way it does.

There are several interpretations of QM all different all give the same results so there is know way of telling which is right. We kick out the ones that don't give the right results!

In classical physics we can have an intuitive feel for its idealised objects. Point masses with velocity and position etc. However, this is not true in QM and when we impose our classical ideas it leads to contradictions and paradox.

Still well worth the effort of getting an understanding . I found I had to completely relearn it as it had moved on from my 1970's uni days.

Regards Andrew 

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Posted (edited)

Nigella I would avoid the maths altogether unless it is something you particularly want to do ; I'm going to attract some fire here but it's largely impenetrable probability  based overlaid with its own language and branch of mathematics.   If what you are looking for is an good overview then I would recommend the following book  as a starting point "Six Impossible Things - the quanta of solace and the mysteries of the subatomic world" by John Gribbin.  Very accessible but still challenging -  he looks at 6 different interpretations of Quantum Mechanics to challenge the famous Copenhagen Interpretation.  These different interpretations are themselves all of course flawed in their own way but offer the potential of solace in understanding of what is truly counter intuitive to us.  The discussion of each interpretation is set against an examination of how each explains what goes on in the double slit experiment  ( the experiment with two holes as it was referred to by Feynman).  No equations and very well written - nice little hardback book - was my holiday read :)

Six Impossible Things - The Quanta Of Solace

 

Jim 

Edited by saac
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I've bought two books, quantum universe and six impossible things, so I'll be sorted for the next few weeks, lol. Well, if I can get my head around it, or would that be through it both at the same time, lol. Thanks again everyone. Be prepared for questions when I don't understand things. 

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2 hours ago, Nigella Bryant said:

I've bought two books, quantum universe and six impossible things, so I'll be sorted for the next few weeks, lol. Well, if I can get my head around it, or would that be through it both at the same time, lol. Thanks again everyone. Be prepared for questions when I don't understand things. 

Good luck with the reading Nigella, be prepared to read chapters several times for it to click. I found myself flicking through the same chapter again and again. 

Jim 

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Maybe search out: 30 Second Quantum Theory, editor is given as Brian Clegg.

Gives short background interpretations of the dieeferent aspects and background.

No maths in it that I can see. Useful for just building up a background knowledge, overview or history.

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Marcus Chown has written a number of non-scary introductions to various aspects of particle physics and cosmology.  There's a bit of crossover between some of them, unavoidably perhaps.  They avoid the maths and just stick to the general concepts.

James

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On 07/08/2019 at 05:57, vlaiv said:

QM is not that complicated at all, what is problematic to most people is math behind it - you need to understand the math in order to understand the QM.

If you have math knowledge, then there is a very good set of lectures online by Leonard Susskind that cover many aspects of physics including much of QM. Lectures are based on his book and titled the same: Theoretical minimum

There is a website with link to videos of lectures on youtube:

https://theoreticalminimum.com/

I find lectures very good although sometimes a bit slower paced than I would like (some concepts are explained multiple times because lectures are recorded in actual class and people have questions, etc ...).

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

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2 hours ago, DarkAntimatter said:

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

It depends on what you mean by "good understanding" with respect to a mathematical treatment of quantum mechanics.

The most used text for upper-level undergraduate quantum mechanics courses in North America is "Introduction to Quantum Mechanics" by David Griffiths. From its preface: "The reader must be familiar with the rudiments of linear algebra, complex numbers, and calculus up through partial derivatives; some acquaintance with Fourier analysis and the Dirac delta function would help."

A European quantum mechanics course might require more.

The lectures and books that @vlaiv gave above are interesting.

On 07/08/2019 at 02:57, vlaiv said:

If you have math knowledge, then there is a very good set of lectures online by Leonard Susskind that cover many aspects of physics including much of QM. Lectures are based on his book and titled the same: Theoretical minimum

There is a website with link to videos of lectures on youtube:

https://theoreticalminimum.com/

I find lectures very good although sometimes a bit slower paced than I would like (some concepts are explained multiple times because lectures are recorded in actual class and people have questions, etc ...).

From the website: "A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology.  Fat advanced textbooks are not suitable to people who have no teacher to ask questions of, and the popular literature does not go deeply enough to satisfy these curious people.  So I started a series of courses on modern physics at Stanford University where I am a professor of physics.  The courses are specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners."

I might be able to find references

that use some math, but less math than the above.

On 07/08/2019 at 02:57, vlaiv said:

QM is not that complicated at all, what is problematic to most people is math behind it

Our intuition is based largely on our experiences. Quantum mechanics is also mind-stretching because it so counter-intuitive, as many quantum phenomena are far away from everyday experience. Some of this can be discussed without maths.

11 hours ago, saac said:

Good luck with the reading Nigella, be prepared to read chapters several times for it to click. I found myself flicking through the same chapter again and again.

I often have to this.

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Thank you. By "good understanding" I meant what particular math so that QM becomes not very complicated. I expect that will mean more than algebra, ode, and some Fourier analysis. 

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2 minutes ago, DarkAntimatter said:

Thank you. By "good understanding" I meant what particular math so that QM becomes not very complicated. I expect that will mean more than algebra, ode, and some Fourier analysis. 

Actually no, that is what you in principle need:

- calculus

- algebra (meaning algebraic structures like vector spaces and groups/rings/ ....)

- Fourier analysis

- complex numbers

Important thing is ability to think in abstract terms - which should be covered by second above - algebraic structures. Most of QM formalism is expressed in these abstract structures. For example, when we speak about vector spaces - most people imagine plain old vectors - little arrows that have origin, direction and magnitude. But vector space does not mean those vectors - it can mean space of real functions where you can use certain operations on members of the space. Vectors are thus members of a set - or in simple terms some entities that behave in certain way.

Here is what wiki lists as set of math tools needed:

image.png.3be7a45847aeeeb27df5dde127272f6d.png

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1 hour ago, vlaiv said:

Actually no, that is what you in principle need:

- calculus

- algebra (meaning algebraic structures like vector spaces and groups/rings/ ....)

- Fourier analysis

- complex numbers

Important thing is ability to think in abstract terms - which should be covered by second above - algebraic structures. Most of QM formalism is expressed in these abstract structures. For example, when we speak about vector spaces - most people imagine plain old vectors - little arrows that have origin, direction and magnitude. But vector space does not mean those vectors - it can mean space of real functions where you can use certain operations on members of the space. Vectors are thus members of a set - or in simple terms some entities that behave in certain way.

Here is what wiki lists as set of math tools needed:

image.png.3be7a45847aeeeb27df5dde127272f6d.png

Thanks, that is a good list.  My background is as an engineer so I have a (very) little bit of familiarity with the above.  But I found it slow going when things turned to Pauli (which seem to be important to really understand spin), and especially gamma (Dirac) matrices.  I was not sure if this is something that I should just be expected to learn from the information in the QM book or if there is a particular math subject that would cover this better.  

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1 hour ago, DarkAntimatter said:

Thanks, that is a good list.  My background is as an engineer so I have a (very) little bit of familiarity with the above.  But I found it slow going when things turned to Pauli (which seem to be important to really understand spin), and especially gamma (Dirac) matrices.  I was not sure if this is something that I should just be expected to learn from the information in the QM book or if there is a particular math subject that would cover this better.  

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.

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Posted (edited)

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

 

Edited by andrew s
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