Physical Significance Of Error Function
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Error Function Calculator
Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes error function table a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top What is the significance of error function? up vote 1 down vote error function matlab favorite 1 Here's a Wiki article on the subject. Sadly it doesn't do a good job of explaining the significance of the function. Of course it may mean different things to different people (for mathematicians it may be important for reasons entirely different from the reasons it is important to engineers). The following is a hypothetical problem explaining the significance I am looking for. A laser printer has a targeting system where a laser is supposed to mark a paper
Inverse Error Function
at say x=6cm. The standard deviation measured on a large number of attempts to mark the ordinate turns out to be 0.1 cm. If say a billion attempts are made to target x=6cm, what is the maximum expected ordinate that will be marked? Does the error function help me in solving such problems? probability probability-theory probability-distributions error-function share|cite|improve this question asked Aug 29 '12 at 18:47 Shashank Sawant 17411 1 It is closely---trivially---related to the cumulative distribution function of the standard normal distribution. –Michael Hardy Aug 29 '12 at 21:23 1 Error function usually does not help you to do something. It is not an equation you get and use it. It comes out from the derivations of your own problem. Almost all such problems have exponentials. –Seyhmus Güngören Aug 29 '12 at 21:51 You do not explain why the Wiki article on the subject would not do a good job of explaining the significance of the function. Care to expand? –Did Oct 14 '12 at 10:38 I would like to contrast that with the wiki article on normal distribution (en.wikipedia.org/wiki/Normal_distribution). It does a really good job of explaining how normal function is relevant and how it affects numerous physical phenomena. Here I am referring to the the subsections "Occurrence" and "History", which in my opinion do justice to the subject. The error function just has a small subsection (en.wikipedia.org/wik
meaning of error function in quantum mechanics?UpdateCancelAnswer Wiki1 Answer David Moore, Currently a UCSD senior year undergraduate in physics.Written 94w agoBecause the fundamental solution of the (free space V=constant) Schroedinger equation error function excel is a Gaussian. (cf Wave packet blue boxed equation). So any question error function python of probabilities of a fundamental solution will be the magnitude of the gaussian (which is again a gaussian), integrated. Which
Inverse Error Function Excel
is erf. In more algebraically complex situations (ie, not a pure Gaussian), the simplest solutions will usually be studied, and those will likely have a Gaussian in them.This is easy to see http://math.stackexchange.com/questions/188506/what-is-the-significance-of-error-function from calculus and algebra.Once you have the Gaussian, you have erf. The real question would be, why is the fundamental solution of the free space Schroedinger equation a Gaussian, and what deeper physical meaning does it have? Of course the Gaussian is special for several reasons (like the central limit theorem), but how does it come up in quantum mechanics?This can be answered with the https://www.quora.com/What-is-the-physical-meaning-of-error-function-in-quantum-mechanics stunning path integral formalism, but I don't know enough to comment here. I can however recommend: Cox & Foreshaw: http://www.amazon.com/The-Quantu... (Good reading for a general audience. This book discusses the path integral formalism first, though it doesn't use that name.)This lecture series of Feynman, which at first may seem unrelated to the topic at hand, but it lays the foundation. This is for a general audience. The Vega Science Trust (my favorite lecture by Feynman)Statistical Mechanics: Algorithms and computations. https://www.coursera.org/course/... This course covers (or the book of the same title) the path sampling needed to computationally understand how a path integral can give rise to a gaussian. This link is useless for those not wanting to put in a lot of time or program in python (the course uses python).515 Views · View UpvotesView More AnswersRelated QuestionsWhat is the physical significance of error function?What is the error function and why is it useful in physics?What is the physical meaning of "potential well" in quantum mechanics?What is particle spin?What is the physical meaning of normalization of a wave function in quantum mechanics?What is physical quantity in quantum mechanics mean?In quantum mechanics, what physic
that occurs in probability, statistics, and partial differential equations describing diffusion. It is defined as:[1][2] erf ( x ) = 1 π ∫ − x x e − https://en.wikipedia.org/wiki/Error_function t 2 d t = 2 π ∫ 0 x e − t 2 d t . {\displaystyle {\begin − 6\operatorname − 5 (x)&={\frac − 4{\sqrt {\pi }}}\int _{-x}^ − 3e^{-t^ − 2}\,\mathrm − 1 t\\&={\frac − 0{\sqrt {\pi }}}\int _ 9^ 8e^{-t^ 7}\,\mathrm 6 t.\end 5}} The complementary error function, denoted erfc, is defined as erfc error function ( x ) = 1 − erf ( x ) = 2 π ∫ x ∞ e − t 2 d t = e − x 2 erfcx ( x ) , {\displaystyle {\begin 2\operatorname 1 (x)&=1-\operatorname 0 (x)\\&={\frac Φ 9{\sqrt {\pi }}}\int _ Φ 8^{\infty }e^{-t^ Φ 7}\,\mathrm Φ 6 t\\&=e^{-x^ Φ 5}\operatorname Φ 4 (x),\end Φ 3}} inverse error function which also defines erfcx, the scaled complementary error function[3] (which can be used instead of erfc to avoid arithmetic underflow[3][4]). Another form of erfc ( x ) {\displaystyle \operatorname 2 (x)} for non-negative x {\displaystyle x} is known as Craig's formula:[5] erfc ( x | x ≥ 0 ) = 2 π ∫ 0 π / 2 exp ( − x 2 sin 2 θ ) d θ . {\displaystyle \operatorname 0 (x|x\geq 0)={\frac Φ 9{\pi }}\int _ Φ 8^{\pi /2}\exp \left(-{\frac Φ 7}{\sin ^ Φ 6\theta }}\right)d\theta \,.} The imaginary error function, denoted erfi, is defined as erfi ( x ) = − i erf ( i x ) = 2 π ∫ 0 x e t 2 d t = 2 π e x 2 D ( x ) , {\displaystyle {\begin Φ 0\operatorname − 9 (x)&=-i\operatorname − 8 (ix)\\&={\frac − 7{\sqrt {\pi }}}\int _ − 6^ − 5e^ − 4}\,\mathrm − 3 t\\&={\frac − 2{\sqrt {\pi }}}e^ − 1}D(x),\end − 0}} where D(x) is the Dawson function (which can be used instead of erfi to avoid arithm
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