For example, the plane wave solution to the wave equation is not normalisable, so it is not possible to give a physical interpretation of it for a single particle.

They are based on the same inner product and are states normalizable with respect to it.

This function is modeled in several ways, but must always be normalizable and differentiable.

A wavefunction is said to be normalizable if .

All problems mentioned above can be handled by using a normalizable sigmoid activation function.

First, since all 'physical' quantum states are normalizable, one can carefully avoid non-normalizable states.

A normalizable wavefunction can be made to be normalized by .

We then apply the boundary conditions, where and are continuous and the wave function is normalizable:

The wavefunction is not normalizable for a plane wave, but is for a wavepacket.

The momentum operator is always a Hermitian operator when it acts on physical (in particular, normalizable) quantum states.

The two solutions to the indicial equation are and of which the former is taken as it yields the regular (bounded, normalizable) wave function.

The first reason is that the constant function is not normalizable, and thus is not a proper probability distribution.

In addition, networks constructed using this model have unstable convergence because neuron inputs along favored paths tend to increase without bound, as this function is not normalizable.

In the first case, a constant, or any more general finite polynomial, is normalizable within any finite range: the range [0,1] is all that matters here.

In the mathematical formulation of quantum mechanics, a physical system is fully described by a vector in a complex number Hilbert space, the collection of all possible normalizable wavefunctions.

This comes at the price that the solutions must be given a new Hilbert space inner product with respect to which they are normalizable (see article on rigged Hilbert space).

The usual priors such as the Jeffreys prior often do not work, because the posterior distribution will be improper (not normalizable), and estimates made by minimizing the expected loss will be inadmissible.

The correct prescription, as developed by Lehmann, Symanzik and Zimmermann, requires two normalizable states and , and a normalizable solution of the Klein-Gordon equation .

Randono concluded that the Immirzi parameter, when generalized with a real value, fixed by matching with black hole entropy, describes parity violation in quantum gravity, and is CPT invariant, and is normalizable, and chiral, consistent with known observations of both gravity and quantum field theory.