Examples of 'eigenfunctions' in a sentence
Meaning of "eigenfunctions"
eigenfunction (noun) - in mathematics, an eigenfunction of a linear operator is a non-zero function that returns from a given function only a constant multiple of that function
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- plural of eigenfunction
How to use "eigenfunctions" in a sentence
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eigenfunctions
Eigenvalues and eigenfunctions of an integral homogeneous equation.
Each value of λ corresponds to one or more eigenfunctions.
Eigenfunctions are required in order to embed a given manifold.
As these must also be eigenfunctions of the operator.
The eigenfunctions of the transfer operator are usually fractals.
I must work out some new eigenfunctions.
The eigenfunctions are to satisfy the equation in this.
They are characterized by the exponential shape of their eigenfunctions.
It can also be shown that the eigenfunctions are infinitely differentiable functions.
These correspond to the energy eigenfunctions.
Eigenfunctions of this model have derivative jumps similar to the electronic cusps.
The analysis of these problems involves the eigenfunctions of a differential operator.
The new resonances are associated with different acoustic field distributions or eigenfunctions.
This is a property of delocalization of most eigenfunctions in the large scale limit.
The image to the right shows the first few hydrogen atom orbitals energy eigenfunctions.
See also
From which it is evident that the eigenfunctions must satisfy the conditions.
We obtain accurate second order asymptotic approximations for both the eigenvalues and the eigenfunctions.
Exponentials as eigenfunctions.
The eigenfunctions are the familiar D functions.
This gain is lower than previously but the basis of eigenfunctions are general.
Some structural properties of energy eigenfunctions of two electrons in a simple harmonic potential are analyzed.
Expressions are provided for normalizing the coefficients and extending the eigenfunctions beyond the unit interval.
Results will be shown for eigenfunctions and eigenvalues on angular sectors of various shapes.
H and Sz have the same eigenfunctions.
The derivative jumps of eigenfunctions of the VPAW eigenvalue problem are significantly reduced.
We also studied the number of critical points of Laplace eigenfunctions.
These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum.
In chapter 3 we prove results on pointwise growth of eigenfunctions.
A method for evaluating the eigenvalues and eigenfunctions of this model Hamiltonian is presented.
The energy eigenfunctions are assumed to be products of one-electron wavefunctions.
Often the basis of functions are orthonormal eigenfunctions for some Hermitian operator.
Furthermore, the eigenfunctions are very well approximated in an exponentially weighted space.
The resonances are the poles of a meromorphic family of generalized eigenfunctions of the Laplace operator.
Eigenvalues and eigenfunctions of Hermitian operators.
LTI systems preserve sinusoids as eigenfunctions.
Further, these eigenfunctions are orthogonal.
The Hamiltonian operator H is an example of a Hermitian operator whose eigenfunctions form an orthonormal basis.
Therefore, the independent eigenfunctions that satisfy the boundary conditions are.
Similarly, if you believe in linearity then they are again the eigenfunctions.
However, this choice of eigenfunctions is not unique.
These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis.
In one dimension, it is further proven that these eigenfunctions decay exponentially.
Namely, via the eigenfunctions of the corresponding laplacian or its heat kernel.
These equations have multiple solutions, or modes, which are eigenfunctions of the equation system.
The square pyramidal d3 symmetry eigenfunctions are constructed from the one-electron crystal field eigenfunctions.
It is demonstrated that the periodicity of the probability density implies periodic or anti-periodic eigenfunctions.
In such a case, we need to distinguish between the eigenfunctions corresponding to the same eigenvalue.
The eigenfunctions of the position operator, represented in position space, are Dirac delta functions.
Mathematically, finding these modes requires to seek the eigenvalues and eigenfunctions of the propagation operator.
Its eigenfunctions form a basis of the function space on which the operator is defined [ 5 ].
