Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Boundary conditions for the wave functions and Gamow vectors

Piotr Kielanowski

Published Mar 1, 2011• 0 citations
Publisher

Abstract

We introduce a new kind of boundary conditions for the wave functions, which admit solutions in the form of Gamow vectors for a wide class of potentials. We discuss in detail an example of an unstable quantum oscillator.
DOI
10.1088/1742-6596/284/1/012037

Related papers

Time-Reversal and Irreversibility

Arno Böhm, Piotr Kielanowski

The time reversal and irreversibility in conventional quantum mechanics are compared with those of the rigged Hilbert space quantum mechanics. We discuss the time evolution of Gamow and Gamow-Jordan vectors and show that the rigged Hilbert space case admits a new kind of irreversibility which does not appear in the conventional case. The origin of this irreversibility can be traced back to different initial-boundary conditions for the states and observables. It is shown that this irreversibility does not contradict the experimentally tested consequences of the time-reversal invariance of the conventional case but instead we have to introduce a new time reversal operator.

arXiv:quant-ph/9512014•Dec 12, 1995•0 citations

On the Boundary conditions for the Radial Schrodinger Equation

Anzor Khelashvili, Teimuraz Nadareishvili

Exploring the idea that equation for radial wave function must be compatible with the full Schrodinger equation, a boundary condition is derived.

arXiv:1001.3285•Jan 19, 2010•1 citation

The Functional Integrals for Quantum Systems with Boundary Conditions and with Hamiltonians Unbounded from Below

Michel Carreau

•Jan 1, 1991•0 citations

The Rigged Hilbert space formalism in quantum mechanics with applications to higher-order pole resonances and to potential barriers

C. Püntmann

In the first part, Gamow vectors from S-matrix poles of higher multiplicity are derived in analogy to the Gamow vectors describing resonances from first-order poles. With these vectors a density operator is constructed that describes resonances associated with higher-order poles that obey an exponential decay law. It turns out that this operator formed by higher-order Gamow vectors has a unique structure. In the second part, the Gamow vectors are used in order to describe decaying and resonance states at a potential barrier of finite width. The exact numerical solutions of the S-matrix poles are presented and the out-going boundary condition for the Gamow vector description and consequences from that are discussed.

•Jan 1, 1999•0 citations

On Boundary Conditions for an Infinite Square-Well Potential in Quantum Mechanics

Ryoichi Seki

A well-known problem of an infinite square-well potential in quantum mechanics furnishes an interesting boundary condition. We investigate this in detail by considering the infinite square-well potential as a limiting case of an finite square-well potential.

American Journal of Physics•Aug 1, 1971•8 citations

Gamow vectors and Supersymmetric Quantum Mechanics

Óscar Rosas-Ortiz

Gamow solutions are used to transform self-adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non-hermitian operators admit a discrete real spectrum which is occasionally extended by a single complex eigenvalue associated to normalized eigensolutions. These new Hamiltonians are not pseudo-hermitian operators and also differ from those obtained by means of complex-scaling transformations. As an example, Coulomb-like potentials are studied.

arXiv:0810.2283•Revista Mexicana de Física•Oct 13, 2008•10 citations
The time reversal and irreversibility in conventional quantum mechanics are compared with those of the rigged Hilbert space quantum mechanics. We discuss the time evolution of Gamow and Gamow-Jordan vectors and show that the rigged Hilbert space case admits a new kind of irreversibility which does not appear in the conventional case. The origin of this irreversibility can be traced back to different initial-boundary conditions for the states and observables. It is shown that this irreversibility does not contradict the experimentally tested consequences of the time-reversal invariance of the conventional case but instead we have to introduce a new time reversal operator.
In the first part, Gamow vectors from S-matrix poles of higher multiplicity are derived in analogy to the Gamow vectors describing resonances from first-order poles. With these vectors a density operator is constructed that describes resonances associated with higher-order poles that obey an exponential decay law. It turns out that this operator formed by higher-order Gamow vectors has a unique structure. In the second part, the Gamow vectors are used in order to describe decaying and resonance states at a potential barrier of finite width. The exact numerical solutions of the S-matrix poles are presented and the out-going boundary condition for the Gamow vector description and consequences from that are discussed.