In this talk we consider the time evolution of a one-dimensional quantum system with a double barrier given by a couple of repulsive Dirac’s deltas. In such a pedagogical model we give, by means of the theory of quantum resonances, the asymptotic behavior of (Formula Found) for large times, where H is the double-barrier Hamiltonian operator and where ψ and ϕ are two test functions. In particular, when ψ is close to a resonant state then explicit expression of the dominant terms of the survival probability defined as (Formula Found) is given.
Double-barrier resonances and time decay of the survival probability: A toy model / Sacchetti, Andrea. - 18:(2017), pp. 283-293. ( INdAM International Meeting on Contemporary Trends in the Mathematics of Quantum Mechanics Rome, ITALY JUL 04-08, 2016) [10.1007/978-3-319-58904-6_17].
Double-barrier resonances and time decay of the survival probability: A toy model
SACCHETTI, Andrea
2017
Abstract
In this talk we consider the time evolution of a one-dimensional quantum system with a double barrier given by a couple of repulsive Dirac’s deltas. In such a pedagogical model we give, by means of the theory of quantum resonances, the asymptotic behavior of (Formula Found) for large times, where H is the double-barrier Hamiltonian operator and where ψ and ϕ are two test functions. In particular, when ψ is close to a resonant state then explicit expression of the dominant terms of the survival probability defined as (Formula Found) is given.
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