Talk:Quantum state

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[edit] too technical

The page is nice but it's a bit too technical for non-physics (like me!). Can it be rewritten with more user-friendliness, without perhaps sacrificing completeness?

It would really be nice to see some more on what quantumphysical characteristics of particles define their quantum states.

Technical point: The description of the quantum state as formal and non-physical, as against 'real' measurements, is highly debatable. In many accounts of quantum measurement the quantum state (density matrix) is the _only_ physical reality, the results of a measurement also being expressed in terms of a quantum state. Since everything in the Universe is quantum, including the measuring devices, the idea that the result of a measurement is somehow more 'real' can only be a shorthand for the particular type of quantum state which is produced by interactions with a measuring device and the environment.

The page as it stands gives only an old-fashioned Copenhagen-like account of measurement, which by itself is incomplete and unsatisfactory since it doesn't describe what constitutes a measurement and how the system interacts with what's measuring it.

Unfortunately quantum mechanics is the sort of subject where there is no simpler statement of meaning. Quantum states are mathematical formalities which are manipulated using (more) mathematics to gain information on real-world properties. They are not visualisable phenomena in themselves. As has been said, the reality of quantum mechanics is hotly debated and I don't think anyone has yet come up with a satisfactory answer. It's worth noting that 'quantum mechanics' in itself is not a complete theory; it works best when extended with Quantum Field Theory, which makes a little more sense though is even more complicated. 81.156.75.42 11:44, 2 April 2007 (UTC)

[edit] Uncertainty principle

I'm no expert but I think this sentance "Doing this, we determine the initial position q and the initial momentum[1] p" seems to contradict the heisenberg uncertainty principle, that we cannot know the position AND momentum at the same time. —The preceding unsigned comment was added by 138.251.252.7 (talk) 23:22, 12 May 2007 (UTC).

[edit] Huh?!

I dont know a quark about this theme, but I will like to. I think that after this sentence: "A quantum state is any possible state in which a quantum mechanical system can be.", should come a brief explanation about of those possible states or at least some examples. And then the rest: "A fully specified quantum state can be described by a state vector, a wavefunction, or a complete set of quantum numbers for a specific system."

I agree about the first sentence mentioned above: the opening sentence of the article seems tautologous, and it doesn't become clearer until one reaches the Superposition and Pure/Mixed sections.

Seems tautologous? I've seen billiard balls that weren't as circular as that sentence! "In quantum mechanics, a quantum state is any possible state in which a quantum mechanical system can be." Well, that clears it right up. Gee, thanks. And I suppose the science of physics is the branch of science that deals with physics.
I agree that this article is unclear. It certainly didn't give me the information I was looking for. Fresheneesz 02:28, 22 May 2006 (UTC)
This article is the most impenetrable I've ever seen on Wikipedia, and that's saying something.
The tautology in the opening sentence here is unfortunate, but mostly unavoidable. If any Wikipedian can come up with a precise, friendly definition of a quantum state, then I'd give them a hearty slap on the back, because the fact is that no such definition exists. Quantum mechanics is somewhat self-referential in that respect. A state is how something is. Two states are the same if there is no way to tell them apart via a measurement. That's about the sum of it. Between this and the fuzziness of the definition of 'measurement', you'll find that circular logic is just about unavoidable when dealing with the fundamentals of QM.

[edit] Antimatter

Could someone who knows enough about it please add something about the quantum state necessary for antimatter and matter to annihilate with each other when they come into contact with one another? Thanks!

scienceman 23:18, 23 March 2006 (UTC)


IMHO that would be misplaced in this context, this page being a general description of states in quantum theory. Matter / antimatter states are a specific feature of quantum field theory (i.e. quantum theory + special relativity), and annihilation processes are in fact a question of scattering theory (or of the interaction of the system, if you like), not of the quantum state. See Antiparticle and PCT Theorem.

--B. Wolterding 12:00, 30 April 2007 (UTC)

[edit] Merge with excited state, and Energy level

I think it would be a good idea to merge Energy level and excited state with this page. They are all very related concepts, and excited state in particular is a trivial subset of the quantum states - and could easily be a simple section on this page. Any comments? Fresheneesz 02:35, 22 May 2006 (UTC)

I might support making stationary state, energy level, excited state and ground state into the same article. (I think if you want to suggest any of those mergers, then you have to do all of them). On the other hand, I think it's too much to merge it into this article (quantum state). Rather, this article should have a section on stationary states, with a {{main|stationary state}} tag linking to the big article about eigenstates of the hamiltonian (strictly speaking, I think an energy level is an eigenvalue, not an eigenstate, so it's not a quantum state, right? so the proper article to link to is stationary state, not energy level). -lethe talk + 02:45, 22 May 2006 (UTC)
Sounds like a good plan. I don't know when i'd get to doing that tho. I'll try to start a merge of some of those soon. Fresheneesz 06:00, 22 May 2006 (UTC)
Looking at the articles, I've come to the opinion that energy level should not be merged. There is simply too much to say about calculation of energy levels. So I guess I'm left considering a merger of stationary state, excited state, and ground state. -lethe talk + 15:50, 22 May 2006 (UTC)
I merged ground level and stationary state, but I don't think theres a good way of merging excited state as well - unles its merged here (quantum state). I don't see a problem with merging those here, its not that much info. And, they all fall under the category of quantum states. Fresheneesz 02:27, 23 May 2006 (UTC)


Please DO NOT merge energy level with quantum state. A quantum state is a distinct entitity, with a number of observables, only one of which is it's (eigen) energy. The energy level entry needs improvement, and should state something like the following: "Multiple states may have the same value of the energy, in which case they are called degenerate states." For example, there are four distinct n=2 states in hydrogen (one 2s, three 2p). In the absence of any external field, they are precisely degenerate. They form an energy level. However, they are quite clearly not the same quantum state, as they result in different values for other observables, such as the electron's angular momentum, or it's projection. Thus, and energy level can contain many quantum states and it is not appropriate to merge this topic with the quantum state topic. I propose we remove the suggestion to merge the energy level article with this one. Az7997 19:08, 2 June 2006 (UTC)
oppose merger quantum state is a specific universe of physics theory. excited states exist in classical mechanics and thermosdynamics. a merger would be nonsense Anlace 03:07, 18 September 2006 (UTC)

[edit] Keep'em seperate

I'm not a total science person, but I know enough to know that they should probably be kept seperate. I think the beauty of wikipedia is to have as much detail as possible on different pages. As long as the topics are well-linked, the info is accessable.

65.211.131.10 21:24, 9 June 2006 (UTC)

oppose merger quantum state is a specific universe of physics theory. excited states exist in classical mechanics and thermosdynamics. a merger would be nonsense Anlace 03:06, 18 September 2006 (UTC)

[edit] Background info added

I added a link to NASA to the excited state page to help make the information a little more user-friendly. That might also be a good base reference for anyone who wanted to make the wikipage more basic/complete.

[edit] Not clear

"All experimental predictions (?) are based on the quantum state of the system and the quantum operations acting on the state. ": it is not clear to me.Sangak 19:41, 5 February 2007 (UTC)


new first paragraph -

At the outset it could be made clear that this is a mathematical description using statistics to describe experimental results. It should not be confused with being an actual representation of anything real. 220.101.73.119 23:40, 10 March 2007 (UTC)bluehigh

[edit] Conceptual introduction

It has been remarked that this article was very technical. I have tried to fix this by adding a "conceptual description" that includes only minimal technicalities. The drawback is that the article is now rather lengthy.

Maybe there are still some aspects missing (due to brevity). Maybe parts of that description might be moved to State (physics). Comments are appreciated.

Supposing that no one protests, I would also like to update the summary and part of the second section, which are now a bit out-of-sync with the new (first) one. I would also add some details to the last section "mathematical description"; just the reference to "GNS construction" is not quite what one would expect.

In my opinion, the "concept" template can be removed now. Any opinions? --B. Wolterding 15:41, 6 May 2007 (UTC)

i think the section you added is fine, although it could be more succinct, and gives sufficient reason to remove the "context" template, the problem with the intro pointed out by Steve below notwithstanding. the neglected state of the "mathematical formulation" section can probably be blamed on me. if it does get fleshed out, perhaps a good remark to include would be that, given an algebra of classical or quantum observables, a physical state is a positive linear functional on the algebra. Mct mht 05:47, 25 October 2007 (UTC)
The conceptual introduction is excellent. It provides an explanation of quantum states in relation to classical mechanics in a way that's very accessible to a layman (like myself). In fact, it's one of the best explanations of this type I've seen. And it's even structured properly: general aspects first, technical aspects later. It's extremely frustrating to see mathematical or physics wiki articles that begin with technical jargon. Well done. RabidDeity (talk) 01:23, 11 April 2008 (UTC)

[edit] Inaccuracy in intro?

The intro states, "For example, in the case of a single particle in a one dimensional box, the state of a particle can be defined by a single quantum number related to the energy of this particle." A general quantum state is a superposition of every energy eigenstates, each with a potentially different complex coefficient, so the state characterized only by an infinite sequence of complex numbers, right? Or am I misunderstanding how the term "quantum state" is being used? --Steve 21:40, 24 October 2007 (UTC)

i think you're right. the article agrees with you, except in the intro. it's not clear to me what the quoted statement is saying. in fact, it's not clear at all what most of the introduction is saying. for instance, we have "A fully specified quantum state can be described by...a complete set of quantum numbers...". what does that mean? Mct mht 00:28, 25 October 2007 (UTC)
I agree, the introduction needs to be rewritten. In general the link between the physical concepts and the mathematical objects is not really well explained. I really need to add that "Mathematical formulation" section...
Now for the quantum numbers: What physicists mean here is a label for a basis in the Hilbert space. The link is as follows: Pure states correspond (more or less) to vectors in the Hilbert space. It usually suffices to consider a basis (often, the basis of eigenstates of the energy operator). Mathematicians would write the basis as something like {ψj} with say an integer index j. Physicists just write | j > instead of ψj and call j a "quantum number". If the energy operator does not have degenerate eigenvalues, you can take its eigenvalues as the label j ("the energy as a quantum number"). If it does have degenerate eigenvalues, you need to add other labels to distinguish the basis vectors (example: the eigenvalues of the angular momentum operator), that leaves you with a "set of quantum numbers".
In short, the intro needs a rewrite and I didn't do that when I found the article and added the "conceptual introduction"... But maybe I should. --B. Wolterding 09:21, 25 October 2007 (UTC)
statements such as
the quantum state of a system is a set of numbers that fully describe a quantum system. ...These numbers are called the quantum numbers of the system.
and
A fully specified quantum state can be described by ... a complete set of quantum numbers for a specific system.
is really bad, imprecise, and highly misleading language. i'd be surprised if that's common physicist's jargon. if it is, i suggest it be not used in the article. Mct mht 02:25, 28 October 2007 (UTC)
I rewrote the lead paragraph now. Comments are appreciated. --B. Wolterding (talk) 17:08, 17 November 2007 (UTC)
I think it's on the right track, but I wish there was a better first summary sentence than "a complete description of the parameters of the experiment". When I read this I think, "okay, a quantum state is how much liquid helium I put into the dewar, what brand of monochrometer I'm using, etc.".
I'm thinking, maybe something along the lines of,

The quantum state of a system is a set of numbers that fully describes the quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state. Quantum states can be statistically mixed, corresponding to a experiment involving a random change of the parameters. States obtained in this way are called mixed states, as opposed to pure states which cannot be described as a mixture of others. When performing a certain measurement on a quantum state, the result is in general described by a probability distribution, and the form that this distribution takes is completely determined by the quantum state and the observable describing the measurement. However, unlike in classical mechanics, even the measurement of pure quantum states is only determined probabilistically. This reflects a core difference between classical and quantum physics.

(The first two sentences, I wrote into this article.) Comments? --Steve (talk) 18:01, 20 November 2007 (UTC)

I think this is an improvement on what is there - I like it. I particularly like the statement about the apparatus and procedure that prepares the state. PhySusie (talk) 18:19, 20 November 2007 (UTC)

  • Fine for me in principle, but I disagree with the "set of numbers". (Describing e.g. an L2 function as a "set of numbers" seems like stressing the picture too far.) How about this one:
In quantum physics, the quantum state of a system is a mathematical object that fully describes the quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state; the mathematical object then reflects the setup of the apparatus. (...)
Also, I suggest "measurement of pure quantum states" -> "measurement results in pure quantum states" in the last sentence. --B. Wolterding (talk) 18:28, 20 November 2007 (UTC)

I like the "mathematical object that fully describes the quantum system" part - much nicer. The second recommendation though doesn't work grammatically. PhySusie (talk) 18:46, 20 November 2007 (UTC)

Well, what I wanted to point out is just that not the measurements are probabilistic, but the measurement results. (A very minor point of course.) --B. Wolterding (talk) 15:40, 21 November 2007 (UTC)

Ah! Now I see what you meant - I was reading the word 'results' as a verb and you were using it as a noun - lol - sorry. Maybe use 'the results of measurements of pure quantum states' instead - and its not a minor point, that is important to keep clear. Go for it! PhySusie (talk) 17:29, 21 November 2007 (UTC)