Talk:Probability amplitude/Archive 1

(Tags moved from article page to talk page 29 December 2010)--Physics is all gnomes (talk) 16:52, 29 December 2010 (UTC)[reply]

relationship between amplitude and density[edit]

Can someone explain what is the relationship between probability amplitude and probability density function? Ohanian 00:22, 31 October 2005 (UTC) Ả[reply]

IANAP so please correct me if I'm wrong. This distinction seems too obscure to be made in the intro. In my understanding, a continuous random variable has 0 chance of returning any particular value since there are infinite possible values. So you can't assign a chance to a single value, but you can integrate the probability density function between two points and get a non-zero chance for that (dense) set of values. If the random variable were discrete/quantised then it would return a probability instead of a probability density. "Probability amplitude" is I guess the square root of the probability or probability density. I don't know why. It seems reminiscent of the RMS strategy to avoid imaginary trickery. Craig Pemberton (talk) 06:02, 16 May 2009 (UTC)[reply]
- You're making the distinction between continuous and discrete variables, but the terms probability amplitude and probability density function can both be applied to continuous variables. And the distinction is important, definitely not too obscure for the lead. --Michael C. Price ^talk 08:17, 16 May 2009 (UTC)[reply]
As it says in the very first sentence of the lead, the probability density function is the modulus squared of the amplitude ( $\rho =|\psi |^{2}$ $\rho =|\psi |^{2}$ ). This is not obscure, as under the Born interpretation it represents a huge part of the reason we bother doing any of this. As Michael pointed out, Craig is mixed up, as there is no RMS trickery or anything going on here. To clarify, amplitude and density can both be discrete as well (as the last section demonstrates). To realise why the distinction is important, observe that the wavefunction must be complex (a real version does not have the required behaviour), so we cannot dispense with amplitudes, but we still need to mod them to get an interpretation of our wavefunction (to know where the particle is actually likely to be).— Kan8eDie (talk) 13:42, 16 May 2009 (UTC)[reply]
- Woops. I should really proofread more carefully. I mean the distinction between a probability density and a probability.Craig Pemberton (talk) —Preceding undated comment added 05:43, 18 May 2009 (UTC).[reply]

proof[edit]

any chance of a proof of the probability conservation law? — Preceding unsigned comment added by 24.145.134.26 (talk) 23:05, 20 March 2006 (UTC)[reply]

Wavefunction is a probability amplitude[edit]

This entry is superfluous in that the terms "wavefunction" and "probability amplitude" are synonymous. Also, the quantum continuity equation and the concept of probability current (probability flux) deserve an entry of their own. Does anyone object to dissolving this entry and creating a new one dealing exclusively with probability current in quantum mechanics? --Adfgvx 01:36, 28 December 2005 (UTC)[reply]

Update: I've created a probability current entry which is much more extensive than the treatment here. --Adfgvx 06:38, 28 December 2005 (UTC)[reply]

Is this article about the same thing as a wavefunction ? Becuase if it is, they should be merged. Fresheneesz 06:58, 1 May 2006 (UTC)[reply]

It is also possible to have discrete probability amplitudes, such as in describing spin, so I would not suggest merging the articles. --Qrystal (talk) 21:10, 2 January 2008 (UTC)[reply]

Complex numbers?[edit]

Could you put an explanation of what complex numbers have to do with probability? I'm confused.

Complex numbers don't arise because of probability, the arise because of the probability distribution. Waves are often described by sines and cosines - functions that are inherintly tied to complex numbers. The description of the wavefunction is thus often a complex function - and the wavefunction is related to the probability. Fresheneesz 06:58, 1 May 2006 (UTC)[reply]

The example used in the section "Why is probability amplitude a complex number?" does not explain why the probability amplitude is complex. The math works out exactly the same if you choose 1 and -1 as when you choose i and -i. —Preceding unsigned comment added by 98.235.85.54 (talk) 17:52, 8 January 2011 (UTC)[reply]

You're right of course. The darkest patches could come from 1 and -1, and sometimes do. I'll try to add more explanation, but fear that I might be making it too long. --Physics is all gnomes (talk) 20:26, 8 January 2011 (UTC)[reply]

M-Theory[edit]

It may be useful in M-Theory, to consider the mathematical transforms (Laplace/Fourier/Z/s) between Probability Amplitude and Probability Frequency, including probability harmonics or probability spectra of histories (Feynman sum over histories- path integral formulation ) between the two, perhaps using a variation Electronics math (as in time vs. frequency domains in spherical harmonics ). That is to say that a given possible history or probability, being one of many, may be likened to (and analyzed as) one frequency on a spectrum of frequencies, with the most probable history being the fundamental frequency and all the other probabilities appear as harmonics (sub and super orders of the fundamental), or spectral ghosts. In the propagation of a history, as in RF Transmissions, there also exists the polarity; right or left circular, rectangular (including mode), elliptical, transnverse, perpendicular, etc. This could be the equivalent of the dimensions of space in M-theory, especially if one considers skin effect and eddy currents within the transmission line to be the equivalent of the curls and folds in the extra dimensions. The theory is there, but someone else needs to do the math. 70.52.212.244 (talk) 02:21, 21 September 2010 (UTC)[reply]

Nov. 2008 rewrite[edit]

I have revamped the article, because I felt we should have some explanation and more general definition for key ideas like this. I feel the article now needs someone to write a bit of general explanation for a layperson on why the association of amplitudes with real probabilities is so seminal (the sort of thing Feynman was good at writing). As far as length goes, this is a pretty simple idea, so we do not want more content, but I fear I am not always clear (properly explained, the example of the continuous wavefunction and the discrete example should be enough to give readers an idea of what an amplitude is). Comments? (Or even better, improvements!) —Kan8eDie (talk) 04:39, 21 November 2008 (UTC)[reply]

(response originally on Kan8eDie's talk page)

I saw your request for review on this article. It's very clear and well-written, for someone with a couple of years of college physics. I like it a lot on that basis, it's thorough and accurate.

I wanted to say it could use a simpler first paragraph, so non-physicists could at least get some idea of what you're talking about. But after making a few attempts I gave up. My next thought was to reference another article that gave the basic idea, that failed as well.

So my conclusion is you've done an excellent job, which unfortunately cannot be integrated into the best level for Wikipedia, at least not by me.

AaCBrown (talk) 03:02, 26 November 2008 (UTC)[reply]

Thanks for that. I could not think of any more elementary ways to put it either. Simply, if you don't know what a probability or complex number is, then you need to read more before expecting to make much use of the article. As first sentences go, it is pretty daunting, but I was aiming to pitch the article as a whole as requiring first-year maths undergrad/second year physics (or however these things work out in other countries). Plenty of pages link here, so it seems to fairly well integrated. I would hesitate to say that the article is finished, but it seems to cover the topic adequately, and I consider my work on it largely done (bar tweaking). —Kan8eDie (talk) 02:02, 27 November 2008 (UTC)[reply]

Reply to Request for feedback[edit]

A good article much more readable than arg ;-). Take the following just as suggestions:

wikilink "probability" and "probability density" in the first sentence.
The second paragraph is about the wave function and should go into the wave function section in my opiniion
In the lead you could compare Classical probability theory (which deals with probabilities only; i.e. no amplitudes) and QM probabilities (where equations (Schrodinger, etc) are in terms of complex amplitudes and the observable probabilities are the modulus square of these amplitudes). This could help readers familiar with classical theory to understand the article.
As an intro to the double slit example, state that a completely real quantum theory does not work, because it cannot account for superposition
I am not sure what: These probability amplitudes have special significance because they assume many of the properties of conventional probability theory that cannot be made to apply in quantum mechanics. should tell me.
"the intuitive interpretation might be" change "the"->"an" or "might be"->"is"
Maybe write down the modulus square of psi_total and mention the mixed/quantum terms that you get
"Non-normalisable states" is not easy to understand at least for me. It needs some more wikilinks/explanations/references for instance to the Siegert wave function. I remember normalising plane waves to unit flux (with a factor 1/sqrt(k) ). Is it already included in this section?
Remove "we".
"Discrete amplitudes" should be extended beyond the example
In the example, define k, kappa
For the simple example it does not matter, but I remember there were some issues if you have plane waves with different k. Then, before matching wave functions at boundaries, one should normalise them to unit flux (with a factor of 1/sqrt(k)).
"continuity of wave functions and their derivatives"?
add some QM book as reference

As I said, the article has no major flaws. Pick whatever you like from these suggestions. bamse (talk) 13:30, 16 February 2009 (UTC)[reply]

Thanks. I will get around to looking at these sometime when I have a spot of free time.— Kan8eDie (talk) 21:52, 16 February 2009 (UTC)[reply]

OKi....[edit]

I was reading this and it was getting really intresting, specially the part were he started to explain how the actual calculation works:

Since each of the four superposed states has a probability of 1/4, the probability amplitude of each state in...

Wait, what? probability aplitude? What is that? .... en.wikipedia.org/wiki/ (ctr+v)

And i get here... and after reading the first paragraph, my reaction is; WHAT. THAA. FACK. What did i read? —Preceding unsigned comment added by 85.226.3.146 (talk) 21:52, 11 November 2010 (UTC)[reply]

Okey, i get superposition.. being in several places at the same time... i think (how in the hell is that real? never mind...) but guys, if i .... im just blown away by this new world, and the article aint helping. —Preceding unsigned comment added by 85.226.3.146 (talk) 21:55, 11 November 2010 (UTC)[reply]

Making more accessible[edit]

I've added some sections (Basic example, and why probability amplitudes are complex numbers) in an attempt to make this article more accessible and useful to non-experts. Feedback would be appreciated.--Physics is all gnomes (talk) 17:00, 29 December 2010 (UTC)[reply]