Talk:Superposition principle

message: It's the mathematical description of wave interference phenomenon. It applies to any type of wave.  The article is incorrect in stating the resultant amplitude of two constructively interfering waves is the sum of the two waves. For two waves that are coherent and in-phase, the resultant amplitude is the sum of the two amplitudes plus 2 times the square root of the product of the two amplitudes.  Check the Wikipedia article on Wave Interference for more information, or any physics text book. musant (talk) 03:13, 10 March 2021 (UTC)
thread_title: Superposition

message: Superposition is a nice idea, like negative numbers, but the theory itself excludes experimental findings by default. If anything observed is only observed in a single state, then all experimentation (by default) DISPROVES the superposition state. Also, the dual slit experiment, when we measure the path of particles, also defines light as a particle. The only thing we don't know is why it appears as a self-interfering wave - which again, is neither support for superposition or wave/particle duality. Wow, I'm really mad at the math and physics communities for glossing over these simple notions in order to make the disciplines more interesting!  — Preceding unsigned comment added by 71.163.19.89 (talk) 00:25, 2 June 2018 (UTC)
thread_title: No way to measure or disprove; this theory excludes the possibility of experimentation.

message: The superposition principle is often cited in mathematics. It would be very helpful to note in what ways the superposition principle is used in math. I don't know enough about it to add it. Fresheneesz 10:24, 11 March 2006 (UTC)
thread_title: Mathematics

message: This article is far too user-unfriendly. I am a great fan of calculus, though I am more enthusiastic about referencing - but this physics article does not have enough physis. Diagrams of superpositioning between two sound waves of same frequency would be great. I know this is the principle of superposition but there is no article titled for linear superposition and what little physics is out there about this is well... little. Considering how useful linear superpositioning is with everyday lives, its amazing that there isn't a FA about it. Tourskin 04:59, 8 March 2007 (UTC)
thread_title:  Mathy 

message: Honestly, I cannot see the advantage of a simplified version which is almost equivalent to the complete one. The complete version is already simple enough. And it is obviously valid in the singular case when the output is zero. So we really don't need to simplify it. Paradoxically, even though your intent is to simplify, you don't get what you want: yes, the first version is slightly (and uselessly) simpler, but the article becomes markedly more complex. The overall effect is definitely negative.
I remind you that unfortunately Wikipedia cannot be used to publish the original ideas and interpretations of the editors, even though in some cases these are helpful. But yes, if and only if the simplified version is used in the literature by some authoritative mathematician of physicist, you should edit the article and explain the application, as you proposed. Otherwise, I propose to delete the first version. 
I hope other editors will share their opinion. Paolo.dL (talk) 11:05, 29 June 2008 (UTC)
replies: text: Hmm, well I see your point about it being harder to read, and I also have no interest in going to the library to find sources. So I'm rewriting it without the simplified version. I'm halfway done, and I'll finish tonight, if that's okay. :-) --Steve (talk) 18:23, 29 June 2008 (UTC)

text: Thanks! The post is inspiring...it (almost) makes me want to try to make good articles into great ones, rather than my usual interest of making horrible articles into mediocre ones. Anyway, I tried again, without mentioning the simplified version as such, and compensated by explaining everything in greater detail. Of course, there's plenty of room for improvement, and feel free to try to do so, or let me know if you think I did anything particularly objectionable. :-) --Steve (talk) 04:01, 30 June 2008 (UTC)

text: I just added that linear is synonymous with homogeneous of degree 1, but I'm actually not sure that's right. For example, f: R^2 --> R, with f(x,y)= either x (if xy>0) or 0 (otherwise) is homogeneous of degree one, but not linear, right? --Steve (talk) 16:48, 30 June 2008 (UTC)
replies: text: I am very sorry. I wrote that too much in a hurry. There are two conditions for linearity of a function or transformation or map: additivity and homogeneity of first degree. And additivity (not homogeneity) is synonimous of superposition property. I apologize. See if you like my edits. I am not 100% sure, but that's what I deduce from linear and linear map. Feel free to undo or correct. Paolo.dL (talk) 22:04, 2 July 2008 (UTC)
replies: text: Looks good to me. --Steve (talk) 23:06, 2 July 2008 (UTC)
thread_title:  The simplified version is useless and makes article less readable 

message: The strength of superposition in finding a general solution to a BVP is best illustrated with several non-zero boundary conditions. I suggest that this is illustrated - but, I'm too busy right now. I could do it maybe in a week or two if no one else takes interest. Tparameter (talk) 04:13, 4 July 2008 (UTC)
thread_title:  BVP 

message: This page seems to imply that superposition is identical to linearity. However, a linear map must have both additivity and homogeneity (of degree 1). That is, 
:f(a_1 x_1+\cdots+a_m x_m)=a_1 f(x_1)+\cdots+a_m f(x_m)
If all you've shown is,
:f(x_1+\cdots+x_m)=f(x_1)+\cdots+f(x_m)
then you have not shown linearity. 
So either:
* The references to linearity should be removed entirely.
* The references to linearity should be augmented with a note about the scaling property.
* The scaling property should be added here (is "superposition" another name for linearity? I don't think so, but this page has scant sources, and so all I can do is guess).
Comments? —TedPavlic (talk) 15:45, 30 January 2009 (UTC)
replies: text: Homogeneity of degree 1 is for all practical purposes a consequence of additivity. For example, say you have an additive function in one variable f(x). Since f(x+...+x)=f(x)+...+f(x), it follows pretty easily that f(ax)=af(x) for any rational number a. What about irrational a? Well, if you assume the axiom of choice, then there are bizarre, incredibly discontinuous, impossible-to-write-down functions that are linear but non-homogeneous. But if there's even one nonzero point at which f is continuous, then it follows that f is homogeneous. People talking about the superposition principle are usually talking about reasonably continuous and well-behaved systems, and in those contexts, homogeneity over real numbers is a consequence of additivity. But you're right that the article could use clarification. --Steve (talk) 19:07, 30 January 2009 (UTC)

text: In pages 2 through 5 of Thomas Kailath's "Linear Systems" (Prentice-Hall, 1980), it's argued that superposition can fail for a linear system.  But a discontinuous, nonhomogeneous function is used in the argument.  To me this further emphasizes the need to include homogeniety in the definition of linearity. Mebden (talk) 09:22, 5 May 2009 (UTC)
thread_title:  Additivity does not imply homogeneity 

message: I like how this article is evolving, thanks!  A quick semantic point: Schrodinger's equation does not "govern" wave behavior.  It "describes" it as stated in the introduction to the main article.  I will change it next week, unless someone wishes to defend the claim that calculation of Schrodinger's equation is the a priori physical cause of wave behavior.  Cheers, Wolfworks (talk) 20:09, 17 November 2011 (UTC)
thread_title:  Quantum superposition 

message: Non-quantum superposition computing usually uses bigger informational encoding, with regions to be filled with superpositional data - it creates bigger chunks of information but for some problems works fine
:: when we get our result, we then can compress the now unnecessarily extended version of our output data  — Preceding unsigned comment added by 2A02:2149:8762:D500:A10A:46B7:5026:A29A (talk) 15:31, 17 February 2018 (UTC)
thread_title:  Non-quantum superposition computing 

message: This probably has a very obvious answer or is just a dumb question, but I can't see why this would not apply.
With the two superposition properties of linear systems [F(x) = ax + c \,] that you mentioned at the start (additive and homogeneous), this is how I'd imagine they would be, given the linear function [F(x)] has a constant [c]:
For Additivity:
F(x_1 + x_2) = a(x_1+x_2) + c \,
F(x_1)+F(x_2) = a(x_1+x_2) + 2c \,
For Homogeneity:
F(bx) = abx + c \,
bF(x) = abx + bc\,
Would someone please explain to me the thing I am missing? Please Correct Me If Im Wrong (talk) 16:44, 31 August 2023 (UTC)
thread_title:  Do Linear Systems Not Contain Constants?