Results 121 to 130 of about 77,145 (154)

Rigged Hilbert Spaces

2016
A considerable part of functional analysis, including the theory of linear operators, particularly the spectral theory, cannot be presented successively without the notion of a rigged Hilbert space.
Volodymyr Koshmanenko, Mykola Dudkin
openaire   +2 more sources

Decaying states in the rigged Hilbert space formulation of quantum mechanics

, 1980
Within the rigged Hilbert space formulation of quantum mechanics idealized resonances (without background) are described by generalized eigenvectors of an essentially self‐adjoint Hamiltonian with complex eigenvalue and a Breit–Wigner energy distribution.
A. Bohm
semanticscholar   +1 more source

Geometry of Rigged Hilbert Spaces

2011
In this chapter we study extensions of symmetric non-densely defined operators in the triplets H+⊂ H ⊂H- of rigged Hilbert spaces. The Krasnoselskiĭi formulas discussed in Section 1.7 are based upon the indirect decomposition (1.33), where deficiency subspaces and the domain of symmetric operator may be linearly dependent.
Sergey Belyi, Eduard Tsekanovskii, Yuri Arlinskii   +2 more
openaire   +2 more sources

Quantum theory in the rigged hilbert space — Irreversibility from causality

, 1998
After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac’s braket formalism, allows ...
Arno Bohm, N. Harshman
semanticscholar   +1 more source

A rigged Hilbert space of Hardy‐class functions: Applications to resonances

, 1983
The explicit construction of a dense subspace Φ of square integrable functions on the positive half of the real line is given. This space Φ has the properties that: (1) it is endowed with a metrizable nuclear topology, (2) it is stable under ...
M. Gadella
semanticscholar   +1 more source

Rigged Hilbert space formalism as an extended mathematical formalism for quantum systems. II. Transformation theory in nonrelativistic quantum mechanics

, 1974
Results of a previous paper are used to obtain a rigorous mathematical formulation of the transformation theory of nonrelativistic quantum mechanics within the framework of rigged Hilbert spaces.
O. Melsheimer
semanticscholar   +1 more source

Partial Multiplication of Operators in Rigged Hilbert Spaces

Integral Equations and Operator Theory, 2005
The problem of the multiplication of operators acting in rigged Hilbert spaces is considered. This is done, as usual, by constructing certain intermediate spaces through which the product can be factorized. In the special case where the starting space is the set of C∞-vectors of a self-adjoint operator A, a general procedure for constructing a special ...
TRAPANI, Camillo, TSCHINKE, Francesco
openaire   +3 more sources

A description of virtual scattering states in the rigged Hilbert space formulation of quantum mechanics

, 1983
We define a pair of Gel’fand triplets Φi ⊆Hi⊆Φ′i, i=1,2, where the linear spaces Φi are formed by suitably chosen entire analytic functions on the Riemann surface associated to the transformation ω=z2.
M. Gadella
semanticscholar   +1 more source

Arrow of Time in Rigged Hilbert Space Quantum Mechanics

, 2004
Arno Bohm and Ilya Prigogine's Brussels–Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics.
R. Bishop
semanticscholar   +1 more source

Irreversibility, Resonances and Rigged Hilbert Spaces

2003
Resonance processes are often considered to be a particular case of irreversible processes both at classical and quantum level. Based upon this idea, in this review we present different approaches to resonances in nonrelativistic Quantum Mechanics as well as the relations among them.
Manolo Gadell, Manolo Gadell, Ioannis Antoniou, Ioannis Antoniou   +3 more
openaire   +2 more sources