Quantum Hamiltonian eigenstates for a free transverse field

Abstract

We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon extensions of the quadratic form of the transverse Laplace operator which are used as a source of spherical basis functions with singularity at the origin. This basis then naturally takes place of the one of plane or spherical waves in the process of Fourrier or spherical variable separation.

arXiv comment22 pages

References in corpus (2)

• Properties of the l=1 radial part of the Laplace operator in a special scalar product
• Spectral properties and self-adjoint extensions of the third power of the radial Laplace operator

Cited by in corpus (1)

• Singular perturbations of a free quantum field Hamiltonian