- Each
value of λ
corresponds to one or more
eigenfunctions. If
multiple linearly independent eigenfunctions have the same eigenvalue, the
eigenvalue is...
-
suitable Hilbert space are used to
study the
behavior of
eigenvalues and
eigenfunctions of
differential equations. For example, the Sturm–Liouville problem...
- energies). It is also
called energy eigenvector,
energy eigenstate,
energy eigenfunction, or
energy eigenket. It is very
similar to the
concept of
atomic orbital...
- an
infinite number of
eigenvalues each with a
unique eigenfunction, and that
these eigenfunctions form an
orthonormal basis of a
certain Hilbert space...
- {\tfrac {d}{dx}}}, in
which case the
eigenvectors are
functions called eigenfunctions that are
scaled by that
differential operator, such as ddxeλx=λeλx.{\displaystyle...
-
modes of
vibration of an
idealized circular drum head.
These modes are
eigenfunctions of a
linear operator on a
function space, a
common construction in functional...
- place. A
function such as x↦eix,{\displaystyle x\mapsto e^{ix},} is an
eigenfunction of the
differential operator −iddx{\displaystyle -i{\frac {d}{dx}}}...
- is an
orthonormal basis of the
Hilbert space L2 that
consists of the
eigenfunctions of the
autocovariance operator. FPCA
represents functional data in the...
- of
basis states, as long as they span the space. If one
chooses the
eigenfunctions of the
position operator as a set of
basis functions, one
speaks of...
-
functions for a
semisimple Lie
group G also
provide a set of
simultaneous eigenfunctions for the
natural action of the
centre of the
universal enveloping algebra...
