Is there any Proof of the Principle of Superposition? Is it just a principle or is it verified experimentally?
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2Being more specific is of utmost necessity... – ubuntu_noob Jan 05 '17 at 06:50
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1I'm not keen on this trend of drive by downvoting that seems to have developed recently. This seems a perfectly good question and doesn't deserve a downvote. It's a beginners question, but a fair one. – John Rennie Jan 05 '17 at 06:59
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1It's not an obvious duplicate, but you should have a look at If we can prove that superposition exists, then why can't we measure it? as I think it more or less answers your question. – John Rennie Jan 05 '17 at 07:02
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@JohnRennie: And surprisingly, that is closed under unclear what you're asking – ubuntu_noob Jan 05 '17 at 07:06
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you mean the superposition of quantum mechanics?If so, then it is the fundamental axioms, so there has nothing to do with proof. – Jack Jan 05 '17 at 07:13
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@JohnRennie The question you linked - gives many examples , not any type of proof that suggests from where it came – InquisitiveMind Jan 05 '17 at 17:24
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@JohnRennie it's not even clear what OP means by "Principle of Superposition". Is OP talking about quantum mechanics, circuits, electric field, vectors in general, or something else? This is not a good question and down votes are to be expected. If OP would like to improve, they should heed the first comment asking for a more specific question. – DanielSank Apr 05 '18 at 19:09
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There are many different versions of the principle of superposition, depending on the area of physics; the two most common are superposition in electromagnetism and in quantum mechanics.
In all cases superposition comes about when the physical quantity is represented by a function $f$ that satisfies an equation of the form
$$L(f) = g,$$
where $L$ is some operator and $g$ a given function, which may be zero; we typically interpret it as some kind of "source" for $f$. For example, the Gauss equation in electrostatics is of this form, with $f$ the electric field $\mathbf{E}$, $L$ the divergence, and $g = \rho/\epsilon_0$. The crucial property is that $L$ be linear, which means that for any two functions $f_1$, $f_2$ and any real number $c$ we have
$$L(f_1 + c f_2) = L(f_1) + c L(f_2).$$
Suppose $f_1$ satisfies the equation with source $g_1$ (so $L(f_1) = g_1$) and $f_2$ satisfies the equation with source $g_2$. Then $f_1+f_2$ satisfies the equation with source $g_1 + g_2$, since
$$L(f_1+f_2) = L(f_1) + L(f_2) = g_1 + g_2.$$
Javier
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