منابع مشابه
Gamow Vectors and Borel Summation
We analyze the detailed time dependence of the wave function ψ(x, t) for one dimensional Hamiltonians H = −∂ x + V (x) where V (for example modeling barriers or wells) and ψ(x, 0) are compactly supported. We show that the dispersive part of ψ(x, t), its asymptotic series in powers of t−1/2, is Borel summable. The remainder, the difference between ψ and the Borel sum, is a convergent expansion o...
متن کاملA Pedestrian Introduction to Gamow Vectors
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...
متن کاملGamow Vectors and Representations of the Poincaré Semigroup
The foundations of time asymmetric quantum theory are reviewed and are applied to the construction of relativistic Gamow vectors. Relativistic Gamow vectors are obtained from the resonance pole of the S-matrix and furnish an irreducible representation of the Poincaré semigroup. They have all the properties needed to represent relativistic quasistable particles and can be used to fix the definit...
متن کاملGamow Vectors in a Periodically Perturbed Quantum System
We analyze the behavior of the wave function ψ(x, t) for one dimensional time-dependent Hamiltonian H = −∂2 x ± 2δ(x)(1 +2r cosωt) where ψ(x, 0) is compactly supported. We show that ψ(x, t) has a Borel summable expansion containing finitely many terms of the form P∞ n=−∞ e i3/2 √ kAk,ne −λkt+nωit, where λk represents the associated resonance. This expression defines Gamow vectors and resonances...
متن کاملAnalysis of resonance production using relativistic Gamow vectors
The calculation of an amplitude involving resonance production is presented. This calculation employs for the resonance state a relativistic Gamow vector. It is used for investigating the question of compatibility of the relativistic Gamow vectors kinematics, defined by real 4-velocities and complex mass, with the stable particle kinematics; or in other words, the integration of the Gamow vecto...
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2008
ISSN: 1742-6596
DOI: 10.1088/1742-6596/128/1/012038