Gamow states as continuous linear functionals over analytical test functions

Bollini, C. G.; Civitarese, O.; Paoli, A. L. De; Rocca, M. C.

doi:10.1063/1.531633

Cited by 34 publications

(42 citation statements)

References 24 publications

(14 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If E is a negative real number (or complex), then there are no coefficients of χ(r; E) in (9) for which the boundary conditions (12) can be satisfied unless they are trivially zero. To be more precise, if E is a complex or a negative real number, the corresponding eigensolution χ(r; E) of Eq.…”

Section: 16mentioning

confidence: 99%

A pedestrian introduction to Gamow vectors

Madrid

Gadella

2002

American Journal of Physics

View full text Add to dashboard Cite

The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrödinger equation, we obtain either eigenvectors corresponding to real eigenvalues and the physical spectrum or eigenvectors corresponding to complex eigenvalues (Gamow vectors) and the resonance spectrum. We show that the poles of the S matrix are the same as the poles of the Green function and are the complex eigenvalues of the Schrödinger equation subject to a purely outgoing boundary condition. The intrinsic time asymmetry of the purely outgoing boundary condition is discussed. Finally, we show that the probability of detecting the decay within a shell around the origin of the decaying state follows an exponential law if the Gamow vector (resonance) contribution to this probability is the only contribution that is taken into account.

show abstract

Section: 16mentioning

confidence: 99%

A pedestrian introduction to Gamow vectors

Madrid

Gadella

2002

American Journal of Physics

View full text Add to dashboard Cite

show abstract

“…By recalling Eqs. (20) and (21), we apply the residue theorem to initial data in Φ ± [18] and get two different expansions in GV:…”

Section: Quantization Of a Damped Motionmentioning

confidence: 99%

“…Despite these mathematical properties have been studied by several authors [18][19][20][21][22][23][24][25], a direct physical evidence of their implications is lacking, even in the simplest case of RHO. In this manuscript, we review the basics of TA-QM and of the GV approach to the RHO.…”

Section: Introductionmentioning

confidence: 99%

Irreversible evolution of a wave packet in the rigged-Hilbert-space quantum mechanics

Marcucci

Conti

2016

Phys. Rev. A

View full text Add to dashboard Cite

It is well known that a state with complex energy cannot be the eigenstate of a self-adjoint operator, as the Hamiltonian. Resonances, i.e. states with exponentially decaying observables, are not vectors belonging to the conventional Hilbert space. One can describe these resonances in an unusual mathematical formalism, based on the so-called Rigged Hilbert Space (RHS). In the RHS, the states with complex energy are denoted as Gamow Vectors (GV), and they model decay processes.We study GV of the Reversed Harmonic Oscillator (RHO), and we analytically and numerically investigate the unstable evolution of wave packets. We introduce the background function to study initial data not composed only by a summation of GV and we analyse different wave packets belonging to specific function spaces. Our work furnishes support to the idea that irreversible wave propagations can be investigated using Rigged Hilbert Space Quantum Mechanics and provides insights for the experimental investigation of irreversible dynamics.

show abstract

“…In three previous papers [1,2,3] we have shown that Gamow-states [4] can be interpreted as Sebastiao e Silva's Ultradistributions [5,6,7], whose proper treatment appeals to Rigged Hilbert Space [8,9,10].…”

Section: Introductionmentioning

confidence: 99%