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Eigenfunction - Wikipedia
In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue . en.wikipedia.org
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3.4: Operators, Eigenfunctions, Eigenvalues, and Eigenstates
A physical observable is anything that can be measured. If the wavefunction that describes a system is an eigenfunction of an operator, then the ... chem.libretexts.org
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Wondering about Eigenfunctions : r/learnmath - Reddit
Eigenfunctions. There are certain linear operators on functions (like the derivative) whose eigenfunctions form a basis of the underlying space. www.reddit.com
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eigenfunction
ˈeigenfunction Physics. [tr. G. eigenfunktion.] A solution of a differential equation possessing solutions only for special values of a parameter.1926 Proc. R. Soc. A. CXII. 661 A set of independent solutions, which may be called eigenfunctions. 1927 [see eigenvalue]. 1938 Nature 16 Apr. 668/1 The h... Oxford English Dictionary
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A mini guide to Eigenfunctions - Dr Rosemary Francis - Medium
Any eigenfunction or eigenstate in a quantum system in respect of an observable property is a state in which that observable has a specific value. rosemaryfrancis.medium.com
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Eigenfunction - an overview | ScienceDirect Topics
If the result of operating on a function with an operator is a function that is proportional to the original function, the function is called an ... www.sciencedirect.com
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Eigenfunction Definition | DeepAI
An eigenfunction is a non-zero function that, when acted upon by a given linear operator, produces a scalar multiple of itself. deepai.org
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Differential Equations - Eigenvalues and Eigenfunctions
In this section we will define eigenvalues and eigenfunctions for boundary value problems. We will work quite a few examples illustrating ... tutorial.math.lamar.edu
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11.1: Definitions - Chemistry LibreTexts
If the result of operating on a function is the same function multiplied by a constant, the function is called an eigenfunction of that operator ... chem.libretexts.org
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Eigenfunctions - GeeksforGeeks
An eigenfunction is defined as the non-zero function in which a linear operator L defined on vector space V is applied resulting in the scalar multiple of ... www.geeksforgeeks.org
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What is an eigenfunction and how does one work? - Quora
An eigenfunction of an operator is a function such that the application of on gives again, times a constant. (49) where k is a constant ... www.quora.com
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Eigenfunction in functional calculus Let $X$ be a complex Banach space, $A\in L(X)$ and $F$ be an analytic function in a neighborhood of $\sigma(A)$. Now I want to show that if $x\in X$ is an eigenfunction of $A$ corr...
Let $F(z) = \sum_{n=0}^\infty a_n (z-\lambda_0)^n$, with $\lambda$ inside the radius of convergence (you could just take $\lambda=\lambda_0$). Then $$ \begin{split} F(A)x &= \left(\sum_{n=0}^\infty a_n (A-\lambda_0 I)^n x\right) \\\ &= \sum_{n=0}^\infty a_n (A-\lambda_0 I)^n x = \sum_{n=0}^\infty a_...
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Eigenfunction and their orthogonality with respect to the weight function The Eigenfunction and their orthogonality with respect to the weight function $\sigma$ is defined as $$\int_{a}^{b}\phi _n\text{(x)}\phi _m\tex...
In which case, the $\tanh(\ldots)\sinh(\ldots)$ are the riven functions, since they are orthonormal, taking an inner product with the $m$-th eigenfunction
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How are eigenfunctions found? Let's stick to the derivative operator and any other operators built up from it. For instance, if $D = \frac{d}{dt}$, then the eigenfunction of $D$ is known to be $e^{at}$, associated wit...
For a minimal example an eigenfunction to the operator ${\bf T = D}^2+2{\bf D}$ on the space of $\\{\sin(x),\cos(x)\\}$.
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Eigenfunctions of a second derivative operator Consider the operator $L :=\frac{-d^2}{dy^2}+ \alpha^2 - K(y)$ on the space of functions $f(y) $ on $H^2(-a,a) \cap H_0^1(-a,a)$. Here $K(y)$ is an even function and $\al...
If $f$ satisfies, $$ -f''+a^2f-K(y)f=\lambda f, \quad f(-1)=f(1)=0. $$ then so do $$ f_{even}=\frac{1}{2}\big(f(x)+f(-x)\big), \quad f_{odd}=\frac{1}{2}\big(f(x)-f(-x)\big). $$ Hence, the eigenspace of our operator is spanned by odd and even eigenfunctions. We shall next show that only one of the tw...
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