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The EMM and the Spectral Analysis of a Non Self-adjoint Hamiltonian on an Infinite Dimensional Hilbert Space

Natália Bebiano, João da Providência

Springer proceedings in physicsJan 1, 20166 citations

Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians

Fabio Bagarello

arXiv:1502.07175Annals of PhysicsMar 4, 201519 citations

Spectral analysis of a selected non self-adjoint Hamiltonian in an infinite dimensional Hilbert space

Natália Bebiano, João da Providência, João P. da Providência

The so-called equation of motion method is useful to obtain the explicit form of the eigenvectors and eigenvalues of certain non self-adjoint bosonic Hamiltonians with real eigenvalues. These operators can be diagonalized when they are expressed in terms of pseudo-bosons, which do not behave as ordinary bosons under the adjoint transformation, but obey the Weil-Heisenberg commutation relations.

arXiv:1509.00653Sep 2, 20150 citations

Mathematical aspects of quantum mechanics with non-self-adjoint operators

David Krejčiřı́k

Jun 6, 20182 citations

Intertwining operators for non-self-adjoint Hamiltonians and bicoherent states

F. Bagarello

This paper is devoted to the construction of what we will call exactly solvable models, i.e., of quantum mechanical systems described by an Hamiltonian H whose eigenvalues and eigenvectors can be explicitly constructed out of some minimal ingredients. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed.This paper is devoted to the construction of what we will call exactly solvable models, i.e., of quantum mechanical systems described by an Hamiltonian H whose eigenvalues and eigenvectors can be explicitly constructed out of some minimal ingredients. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed.

arXiv:1609.07579Journal of Mathematical PhysicsOct 1, 201620 citations

Functional Integral Representation of a Model in QED(Analysis of Operators on Gaussian Space and Quantum Probability Theory)

Fumio Hiroshima

This article presents functional integral representations for the heat semigroups with the infinitesimal generators given by self-adjoint Hamiltonians describing an interaction of a non-relativistic charged particle and a quantized radiation field in the Coulomb gauge without the dipole approximation.Special attention is paid to definition of the "time-ordered Hilbert space-valued stochastic integrals associated with a family of isometries from a Hilbert space t,o another one" and semigroup techniques.Some inequalities are derived, which are infinite degree versions of those known for finite dimensional Schr\"odinger operators with classical vector potentials.This article presents functional integral representations for the heat semigroups with the infinitesimal generators given by self-adjoint Hamiltonians describing an interaction of a non-relativistic charged particle and a quantized radiation field in the Coulomb gauge without the dipole approximation.Special attention is paid to definition of the "time-ordered Hilbert space-valued stochastic integrals associated with a family of isometries from a Hilbert space t,o another one" and semigroup techniques.Some inequalities are derived, which are infinite degree versions of those known for finite dimensional Schr\"odinger operators with classical vector potentials.

数理解析研究所講究録Sep 1, 19950 citations

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

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