Talk:Stationary state

Vacuum

It is not true that the ground state of a quantum field theory is always the vacuum. Indeed, in (for example) non-interacting many-body quantum field theory, the ground state is the state where all the levels are occupied up to the Fermi level. The Fock-space state corresponding to the ground state is hence something like | 1....1 > up to the Fermi level. I propose to clarify that point, by stating that it holds only for QED, QCD or other subnuclear physics quantum field theory.

The article doesn't say this anymore. --Steve (talk) 00:05, 20 March 2011 (UTC)

Re-arrange and sources

Sources are required. To do this I might re-write and move things around a bit so sources and referances can be added better. I will not delete anyone's work. It seems that the Bra-ket notation is used oddly. A time-varying wavefunction is not conventionally written $|\Psi (t)\rangle$, it should be more like $|\Psi ,t\rangle$, or just written in usual function notation $\Psi (x,t)$. I havn't seen it that way at any rate... I'll leave that for now - if no-one objects i'll change it myself to $|\Psi ,t\rangle$ (unless someone else does it before me).--F=q(E+v^B) (talk) 18:16, 26 November 2011 (UTC)

I just realized that wave function are time dependent usually (in the relativistic picture). Why would you remove the notation $|\Psi (x,t)\rangle$ ? Okiokiyuki (talk) 20:41, 1 March 2012 (UTC)

Forget it. The notation $|\Psi (t)\rangle$ is used, it seemed strange to mix bracket notation with function notation until I realized it is used in the literature. I stopped watching this page a long time ago.-- F = q(E + v × B) 09:32, 2 March 2012 (UTC)

Is calculation of transition rates on-topic?

My opinion is that the new section on "Transitions between stationary states" is off-topic and should be deleted. It might be on-topic at a different article, maybe time-dependent perturbation theory or Rabi oscillation, or better yet at Wikiversity. Part of the reason it seems off-topic to me is that it contains an awful lot of text and equations for the amount of understanding gained. The main "piece of understanding" that I think readers will get from the section is: "Here is how to do a very specific type of quantum-mechanical calculation." They also might get (if they read carefully) that "Perturbations of the Hamiltonian can induce transitions between otherwise-stationary states." I like the second lesson, but definitely not the first.

In fact, if it was a section about how, in general, perturbations of the Hamiltonian can induce transitions between otherwise-stationary states, I be very happy about it. That would entail throwing out the "worked example", giving a real-world example or two (e.g. "light can excite an electron in an atom"), stating the general principle, and alluding to the fact that if you want to calculate the exact rates, you would use the Schrodinger equation with the help of time-dependent perturbation theory.

There are usually not many "worked examples" in wikipedia physics articles, see Wikipedia is not a textbook. Of course there can be exceptions but I don't think this is one.

Anyway, what do other people think? --Steve (talk) 14:25, 1 March 2012 (UTC)

Well, I agree that my writing could be off-topic here, I choose this page to edit at first sight because I wanted to put this example into it. I'll try to make it fit in the time-dependent perturbation theory article, maybe, or open a new article. The time-dependent perturbation theory is very complete on the topic, I'll see If I can fit into. Please don't delete it , but at least try to make a new page or move the article, cause otherly it would be a pure waste of time (well, not complete on my side but I'd lost the satisfaction of achievement). I agree fully that a discussion on two levels system that can change of state under an electromagnetic plane-wave perturbation type could be really interesting, by pointing out to the convenient references (namely time-dependant perturbation theory, transition rate formula) then one could end up nicely with the numerical result and a comparison with experiment. Anyway you raise the point of the length in a wikipedia article. Some articles are maybe too lengthy. Should the wikipedia being split into several mid-length article like this one or big pages could be allowed ? Actually I was looking for a real-world example to be useful in conclusion of this article. Thank you for your patience.

Please anyway, take your time to edit it again. Wait for the opinion of other, and definitely you can ask me what to do. I don't want my work to be such a waste if you decide to delete it straightforwardly.

Cheers, the writer Okiokiyuki (talk) 14:38, 1 March 2012 (UTC)

OK that sounds fine. FYI, see Help:Page history if you don't already know about that.

There's a loose guideline on when an article is too long, WP:LENGTH. They say more than 50KB or 10,000 words is usually too long. Physics articles are very rarely that long, they tend to be much much shorter. This one is just 10KB. Problems that occur much more often are:

• Section of an article is too long and dense (i.e. full of equations, requiring full attention to follow). This can scare away readers, very few of whom will want to spend the effort to follow the section in detail. I find that dense sections on wikipedia (unlike a textbook) are best avoided most of the time, or put into special-purpose articles with appropriate titles like Derivation of the Navier–Stokes equations.
• Section of an article is too long such that it is way out-of-proportion to the importance of this topic in the overall subject matter. For example, someone might open the newspaper and read that a new study from University of Whatever has shown that quantum squeezed light can improve a photodetector's signal-to-noise ratio. Then they'll open the wikipedia article on quantum mechanics and add a new section about that new study, not realizing how unimportant this study is in the big picture of quantum mechanics.

My problem with your contribution is both of these: It is too dense, and the detailed calculation is way out-of-proportion to the importance of the topic. I can think of dozens of different quantum-mechanics calculations that are as important and relevant (or even more important and relevant) to the subject of "stationary state" as calculating the transition rate of a two-level system driven by an oscillating electric field. For example, deriving time-independent perturbation theory, deriving the WKB approximation, deriving the stationary states of a square well or harmonic oscillator or hydrogen atom, deriving the density of states for massless particles in a box (and its application to the blackbody spectrum), deriving the σ+ and σ- states of an H2 molecule, and on and on. --Steve (talk) 16:13, 2 March 2012 (UTC)\

I agree generally with you. This article is very specialized, mostly the only topic that could use it is vibrational absorption. Indeed, vibrational potential are modelled in first approximation as an harmonic potential. The final result should be to show that the transition probability is a sinc²(f-f₀) function narrowing with time, that means that the probability to go in the upper level is maximum when the differential between the two level corresponds to the wavelength of the laser. It's fully semiclassic. It is not necessary relevant to wikipedia unless I add more enjoyable stuff as a first part discussing molecular vibration for example and a second part describing a real application. The problem arise from the fact that this calculation comes from a book on vibrationnal spectroscopy. For the other problems, I'll look on the internet if I can find references that could provide such informations before to go ahead. A good point of this article IMHO is that I made effort to keep it very well structured and to remove too lengthy and tedious parts. But the topic is still very specialized as you said. — Preceding unsigned comment added by Okiokiyuki (talk • contribs) 21:35, 9 March 2012 (UTC)

Suggested merge

Anyone up for spilling much of the relevant content (not already in this article) from here (lead of Time independent Schrödinger equation section) into this article, leaving only the statement of the TISE is in that section? Yes - I know I'm responsible for so much overlap, its just a suggestion to take or leave...

P.S. I don't understand perturbation theory calculations (yet - will at some point), which is why I didn't comment above. -- F = q(E + v × B) 17:53, 4 March 2012 (UTC)

Stationarity

It seems like an article on the more general term, 'stationary', in physical science would be warranted. For instance, 'stationary' solutions are often considered in hydrodynamics and thermal/statistical mechanics. All Clues Key (talk) 02:16, 23 September 2012 (UTC)

disambiguation

In this page is fully ommited the explanation of “Stationary state” term as it is comprehended in biology. I think it should be integrated. Thanks. — Preceding unsigned comment added by 78.98.128.242 (talk) 19:13, 5 October 2019 (UTC)

I would like to add that the terms “Equilibrium” and “Stationary state” are well-unified in both physical chemistry and biology. Substantial difference is that stationary state need dissipate the energy to persist. The equilibrium does not need it. It is important because these two terms are frequently mismatched in medicine and/or ecology. — Preceding unsigned comment added by 95.103.126.203 (talk) 09:08, 6 October 2019 (UTC)

Equivalence to Orbitals

The article states that, "In chemistry, a stationary state of an electron is called an orbital; more specifically, an atomic orbital for an electron in an atom, or a molecular orbital for an electron in a molecule." This is not true. An orbital is a Hamiltonian eigenvector only if we consider a one-electron molecule. (And even in this case, we assume the Born-Oppenheimer approximation.) In general, in a multi-electron atom, an orbital is NOT a Hamiltonian eigenvector; rather, it is a mathematical building block used in molecular orbital theory to construct an approximation to the actual molecular eigenvector(s). Quote from Ballhausen and Gray, Chapter 3: "For systems that contain only one electron there is no difference in the molecular-orbital and the total electronic wave function. For many-electron systems, however, there is a considerable difference." Outside of its use as a theoretical tool, the orbital itself has no direct physical significance. This is in contrast to the total wavefunction. Indeed, contrary to what the article says (in the many-electron case, "an orbital is only approximately a stationary state"), an orbital is not even approximately a stationary state in a many-electron molecule; it is a completely different construct.

— Preceding unsigned comment added by 193.63.54.219 (talk) 00:14, 8 March 2013 (UTC)

I think that's fair. I rewrote that part. Is it better now? --Steve (talk) 18:23, 9 March 2013 (UTC)

I think that looks great. Thanks for the quick reply.

One more suggestion--I think the distinction between a one-electron orbital and the total stationary state for a many-electron molecule could still be clearer. For example, the first sentence says, "In chemistry, a concept similar to the stationary state of an electron is called an orbital," and it may be a bit ambiguous as to what a 'stationary state of an [individual] electron' means. How about incorporating an additional paragraph along the lines of the following:

"An orbital is a stationary state (or approximation thereof) of a one-electron atom or molecule; more specifically, an atomic orbital for an electron in an atom, or a molecular orbital for an electron in a molecule.

For a molecule that contains only a single electron (e.g. atomic hydrogen or H₂⁺), an orbital is exactly the same as a total stationary state of the molecule. However, for a many-electron molecule, an orbital is completely different from a total stationary state, which is a many-particle state requiring a more complicated description (such as a Slater determinant). In particular, in a many-electron molecule, an orbital is not the total stationary state of the molecule, but rather the stationary state of a single electron within the molecule. This concept of an orbital is only meaningful under the approximation that if we ignore the electron repulsion terms in the Hamiltonian as a simplifying assumption, we can decompose the total eigenvector of a many-electron molecule into separate contributions from individual electron stationary states (orbitals), each of which are obtained under the one-electron approximation. (Luckily, chemists and physicists can often (but not always) use this "single-electron approximation.") In this sense, in a many-electron system, an orbital can be considered as the stationary state of an individual electron in the system.

In chemistry, calculation of molecular orbitals typically also assume the Born-Oppenheimer approximation." — Preceding unsigned comment added by 193.63.54.236 (talk) 01:55, 12 March 2013 (UTC)

I like it. Copied into article.. --Steve (talk) 19:40, 13 March 2013 (UTC)

Possibly misleading?

"For a single-particle Hamiltonian, this means that the particle has a constant probability distribution for its position, its velocity, its spin, etc.[2]" This sentence could be misleading if the reader takes it to mean you could then measure position and velocity simultaneously. A quantum state is expressed in terms of of a set of commuting variables (preferably a complete set) and position and velocity do not commute. What's a better way to write that sentence? Tonyzitoatdcc (talk) 15:33, 27 April 2017 (UTC)

non-stationary states?

This article seems a fine discussion of stationary states, but somewhere there should be a discussion of non-stationary states. The mixing angle page seems to be only links, and no discussion. There are articles on specific systems, such as Neutrino_oscillation, and there is some discussion in that article, but somewhere there should be general discussion of quantum mechanical mixing, and the resulting non-stationary states. Gah4 (talk) 21:57, 3 October 2019 (UTC)

Orbitals and stationary states not equivalent?

Is it true that a 1s orbital always a stationary state, but a stationary state is not necessarily any kind of orbital? I think that orbitals always involve electrons (and only electrons), while stationary states appear to involve any entity that has energy (that has a nontrivial Hamiltonian). For example, a single photon could have a stationary state, but not an orbital. Yes? The article seems unclear on these points to me. David Spector (talk) 12:14, 17 August 2020 (UTC)