I Any EM-field in terms of photon

ftr

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My problem with using all of these sources is that I cannot understand meaning(theyr relation with physical reality) of mathematical things(operators, brackets) used.
Huh? It's the very basic thing that you'll find in the begining of every quantum mechanics textbook that hermitean operators correspond to measurable quantities and their eigenvalues are the values of that quantity that you can measure in an experiment. The fact that you didn't find that means that you didn't even try to read any textbook. You are wasting your time being reluctant to our advices. There is no other way to learn quantum mechanics and quantum field theory than reading (not glancing through) a proper textbook, period.
 

Demystifier

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Which page of this book explains this specific question?
If he tells you the page, you will find an explanation that contains another concept that you don't understand. If you want to build a house to enjoy the view from the balcony, you must start with building the foundations of the house. The same is with building the understanding of quantum theory. There is no shortcut.
 

vanhees71

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You still don't get it. You won't understand quantum field theory without understanding basics of quantum mechanics, and to learn those basics you need to delve through most of the book, not one or two chapters. There is no other way to understand physics.
That said, maybe you also need some better understanding of classical physics (mechanics and electrodynamics) first. There's no other way to understand physics than to learn it systematically from scratch together with a good deal of math.

For a good understanding of non-relativistic QM you need classical mechanics (including analytical mechanics in the Hamilton version, including Poisson brackets) and some classical electrodynamics (as a first step electrostatics is the minimum in order to understand basic examples like the hydrogen atom). Mathwise you need for sure linear algebra, vector calculus, differential equations, and Fourier transformations.
 

olgerm

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classical electrodynamics (as a first step electrostatics is the minimum in order to understand basic examples like the hydrogen atom). Mathwise you need for sure linear algebra, vector calculus, differential equations, and Fourier transformations.
I know all these things except hamiltonian.
 

olgerm

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I think I just understood something, that I wanted to have explained to me 3 years ago: bra and kets include numbers that describe the states that system can be in. What every number means is not specified, but can vary in every model(must be same everywhere in same model). Is it correct?

Maybe it is misconseption, but I have always thought, that QFT describes particles as fields so that probability of particle being a position is determined by the field value in that point. What ever are relations between these fields are should be describeable by equation between those fields. I cant think of any realtion between fields that can be described by hamilonian, but can not be described by (differencial) equations between the fields. Maybe brackets are more useful in systems that have constraint "forces", but for fields only it should be possible to write it without using hamiltonian.
 
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Quantum mechanics isn’t a change of notation, it’s a fundamentally different physical framework from classical mechanics. You don’t have to use the bra-ket notation but you must learn quantum mechanics to gleam any understanding on the subject.

The Hamiltonian is simply the generator of time-translation (evolving systems forwards/backwards in time) and appears in all frameworks of physics whether directly or indirectly. The classical theory of fields that you seem to be talking about can also be formulated in terms of Hamiltonians but this is not done because it is not as elegant or simple as the Lagrangian approach.
 

olgerm

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Quantum mechanics isn’t a change of notation, it’s a fundamentally different physical framework from classical mechanics. You don’t have to use the bra-ket notation but you must learn quantum mechanics to gleam any understanding on the subject.
I know. I have been looking for sources that do not use bra-ket notation. Even better if it did not use hamiltonian ether.
 
While I question this approach, I guess you could learn QM from the path integral approach first. However it doesn’t seem apparent to me why you shouldn’t learn QM the way everyone else does, since it’s that way for good reason.
 

olgerm

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why you shouldn’t learn QM the way everyone else does, since it’s that way for good reason.
It is not that I do want to learn it in specific way, but that I cant understand the sources that use brakets, operators, and commutivity. I have wanted someone to explain me what these mean or give me clear refence to look it up. I now finally understood something(post 31), but still not enougth.
I dont think any of my learning has been hinder by insufficient knowledge in QM, but by not understanding meaning of brakets, operators, and commutivity.

Is there really something about quantum field that can not be expressed without hamiltonian and brakets, but only by fields and differencial equations?
 
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I dont think any of my learning has been hinder by insufficient knowledge in QM, but by not understanding meaning of brakets, operators, and commutivity.
I don't understand how you can have sufficient knowledge of QM if you don't understand bras and kets, operators, and commutativity, since all of those are basic concepts that are used to describe QM. And, as has already been noted, QM textbooks all go into these subjects. If you work through a QM textbook and find difficulty in understanding something specific it says about bras and kets, operators, or commutativity, you can start a new thread asking about that specific thing. Asking for someone to explain, in general, bras and kets, operators, and commutativity is asking for someone to give you a course in QM, which is way beyond the scope of a PF discussion. If you want such a course, you need to go take one, or find course materials online (for example, MIT's Open Courseware) and work through them.

Thread closed.
 

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