Search results
Results From The WOW.Com Content Network
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.
In this section we will define eigenvalues and eigenfunctions for boundary value problems. We will work quite a few examples illustrating how to find eigenvalues and eigenfunctions. In one example the best we will be able to do is estimate the eigenvalues as that is something that will happen on a fairly regular basis with these kinds of problems.
The function is called an eigenfunction, and the resulting numerical value is called the eigenvalue. Eigen here is the German word meaning self or own. It is a general principle of Quantum Mechanics that there is an operator for every physical observable.
Eigenvalue problems occur naturally in the vibration analysis of mechanical structures with many degrees of freedom. The eigenvalues are the natural frequencies (or eigenfrequencies) of vibration, and the eigenvectors are the shapes of these vibrational modes.
In mathematics, eigenfunction is defined on any function space as some non-zero function f present in that space with linear operator L acted upon it is only multiplied by its eigenvalue. In this article, we will explore the eigenfunction, eigenfunction examples, eigenfunction properties, and applications of eigenfunctions.
D: Eigenvalues and eigenfunctions of an operator are defined as the solutions of the eigenvalue problem: A[un(rx)] = anun(rx) where n = 1, 2, . . . indexes the possible solutions. The an are the eigenvalues of A (they are scalars) and un(rx) are the eigenfunctions.
negative sign and the eigenfunctions will be the same. The reason for using the negative sign is that it tends to make most, if not all, the eigenvalues positive (rather than mostly/all negative); see examples below.
Solutions exist for the time independent Schrodinger equation only for certain values of energy, and these values are called "eigenvalues*" of energy. Corresponding to each eigenvalue is an "eigenfunction*".