Title Non-Hermitian quantum mechanics / Nimrod Moiseyev

Published Cambridge ; New York : Cambridge University Press, 2011

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Description 1 online resource (xiii, 394 pages) : illustrations Contents Cover13; -- Contents13; -- Preface -- 1 Different formulations of quantum mechanics -- 1.1 Hermitian operators: a brief review -- 1.2 Non-Hermitian potentials which support a continuous spectrum -- 1.3 Complex local potentials -- 1.4 Physical interpretation of complex expectation values -- 1.5 Concluding remarks -- 1.6 Solutions to the exercises -- 1.7 Further reading -- 2 Resonance phenomena in nature -- 2.1 Shape-type resonances -- 2.2 Feshbach-type resonances -- 2.3 Concluding remarks -- 2.4 Solutions to the exercises -- 2.5 Further reading -- 3 Resonances from Hermitian quantum-mechanical calculations -- 3.1 Resonances as metastable states -- 3.2 The poles of the S-matrix -- 3.3 Resonances from the spectra of density of states -- 3.4 Resonances from the asymptotes of continuum eigenfunctions -- 3.5 Resonances from the phase shifts -- 3.6 The scattering length -- 3.7 Resonances from stabilization calculations -- 3.8 Decay of resonance states -- 3.9 Real and complex poles of the scattering matrix from wavepacket propagation calculations -- 3.10 Concluding remarks -- 3.11 Solutions to the exercises -- 3.12 Further reading -- 4 Resonances from non-Hermitian quantum mechanical calculations -- 4.1 Resonances for a time-independent Hamiltonian -- 4.2 Transitions of bound states to anti-bound and resonance states -- 4.3 Bound, virtual and resonance states for a 1D potential -- 4.4 The mechanism of transition from a bound state to a resonance state -- 4.5 Concluding remarks on the physical and non-physical poles of the S-matrix -- 4.6 Resonances for a time-dependent Hamiltonian -- 4.7 Conservation of number of particles -- 4.8 Solutions to the exercises -- 4.9 Further reading -- 5 Square integrable resonance wavefunctions -- 5.1 The Zeldovich transformation -- 5.2 The complex scaling transformation -- 5.3 The exterior scaling transformation -- 5.4 The smooth exterior scaling transformation -- 5.5 Dilation of the Hamiltonian matrix elements into the complex plane -- 5.6 Square integrability of field induced resonances -- 5.7 Partial widths from the tails of the wavefunctions -- 5.8 Concluding remarks -- 5.9 Solutions to the exercises -- 5.10 Further reading -- 6 Bi-orthogonal product (c-product) -- 6.1 The c-product -- 6.2 Completeness of the spectrum -- 6.3 Advantages of calculating survival probabilities by c-product -- 6.4 The c-product for non-Hermitian time-periodic Hamiltonians -- 6.5 The F-product for time propagated wavepackets -- 6.6 The F-product and the conservation of the number of particles -- 6.7 Concluding remarks -- 6.8 Solutions to the exercises -- 6.9 Further reading -- 7 The properties of the non-Hermitian Hamiltonian -- 7.1 The turn-over rule -- 7.2 The complex analog of the variational principle -- 7.3 The complex analogs of the virial and hypervirial theorem -- 7.4 The complex analog of the HellmannFeynman theorem -- 7.5 Cusps and 952;-trajectories -- 7.6 Upper and lower bounds of the resonance positions and widths -- 7.7 Perturbation theory for non-Hermitian Hamiltonians -- 7.8 Concluding remarks -- 7.9 Solutions to the exercises -- 7.10 Further reading -- 8 Non-Hermitian scattering theory -- 8.1 Full collision processes for time-independent systems -- 8.2 Half collision processes for time-independent systems -- 8.3 Time-independent scattering theory for time-dependent systems -- 8 Summary "Non-Hermitian quantum mechanics (NHQM) is an important alternative to the standard (Hermitian) formalism of quantum mechanics, enabling the solution of otherwise difficult problems. The first book to present this theory, it will be useful to advanced graduate students and researchers in physics, chemistry and engineering. NHQM provides powerful numerical and analytical tools for the study of resonance phenomena - perhaps one of the most striking events in nature. It is especially useful for problems whose solutions cause extreme difficulties within the structure of a conventional Hermitian framework. NHQM has applications in a variety of fields, including optics where the refractive index is complex; quantum field theory, where the parity-time (PT) symmetry properties of the Hamiltonian are investigated; and atomic and molecular physics and electrical engineering, where complex potentials are introduced to simplify numerical calculations"-- Provided by publisher Bibliography Includes bibliographical references and index Notes English Print version record Subject Quantum theory -- Mathematics Hermitian structures. Resonance. Hermitian symmetric spaces. resonance (acoustics concept) SCIENCE -- Quantum Theory. SCIENCE -- Physics -- Quantum Theory. Hermitian structures Hermitian symmetric spaces Quantum theory -- Mathematics Resonance Quantenphysik -- Mathematische Methode. Form Electronic book ISBN 9780511993152 0511993153 9780511976186 0511976186 1107219396 9781107219397 1282994379 9781282994379 9786612994371 6612994371 0511992122 9780511992124 0511989334 9780511989339 0511987552 9780511987557 0511991142 9780511991141

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