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2017 | OriginalPaper | Chapter

Double-Barrier Resonances and Time Decay of the Survival Probability: A Toy Model

Author : Andrea Sacchetti

Published in: Advances in Quantum Mechanics

Publisher: Springer International Publishing

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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 〈ψ, e −itH ϕ〉 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 | 〈ψ, e −itH ψ〉 |2 is given.

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previous chapter On the Inverse Spectral Problems for Quantum Graphs
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Metadata
Title
Double-Barrier Resonances and Time Decay of the Survival Probability: A Toy Model
Author
Andrea Sacchetti
Copyright Year
2017
Book
Advances in Quantum Mechanics

Print ISBN: 978-3-319-58903-9

Electronic ISBN: 978-3-319-58904-6

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-58904-6_17

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