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Cover  Halftitle  Title  Copyright  Dedication  Contents  Preface  1 Different formulations of quantum mechanics  1.1 Hermitian operators: a brief review  1.2 NonHermitian 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 Shapetype resonances  2.2 Feshbachtype resonances  2.3 Concluding remarks: on the ambiguity of the definitions of shape and Feshbachtype resonances  2.4 Solutions to the exercises  2.5 Further reading  3 Resonances from Hermitian quantummechanical calculations  3.1 Resonances as metastable states  3.2 The poles of the Smatrix  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 nonHermitian quantum mechanical calculations  4.1 Resonances for a timeindependent Hamiltonian  4.2 Transitions of bound states to antibound 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 nonphysical poles of the Smatrix  4.6 Resonances for a timedependent 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 Zel'dovich 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 Biorthogonal product (cproduct)  6.1 The cproduct  6.2 Completeness of the spectrum  6.3 Advantages of calculating survival probabilities by cproduct  6.4 The cproduct for nonHermitian timeperiodic Hamiltonians  6.5 The Fproduct for time propagated wavepackets  6.6 The Fproduct 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 nonHermitian Hamiltonian  7.1 The turnover rule  7.2 The complex analog of the variational principle  7.2.1 Linear cvariational calculations  7.2.2 Nonlinear variational approaches  7.3 The complex analogs of the virial and hypervirial theorem  7.4 The complex analog of the HellmannFeynman theorem  7.5 Cusps and thetatrajectories  7.6 Upper and lower bounds of the resonance positions and widths  7.6.1 The Hermitian representation of the solutions of the nonHermitian timeindependent Schrodinger equation  7.7 Perturbation theory for nonHermitian Hamiltonians  7.8 Concluding remarks  7.9 Solutions to the exercises  7.10 Further reading  8 NonHermitian scattering theory  8.1 Full collision processes for timeindependent systems  8.1.1 The complex coordinate scattering theory and the Kohn variational principle  8.1.2 Resonance scattering: partial widths  8.2 Half collision processes for timeindependent systems 

8.2.1 Wave packet propagation on complex potential energy surfaces  8.3 Timeindependent scattering theory for timedependent systems  8.3.1 Resonance photoinduced ionization decay rates by the nonHermitian formalism of quantum mechanics  8.3.2 The complexscaled resonance wave functions of atoms/molecules in intense timeperiodic laser fields  8.3.3 The nonHermitian adiabatic theorem for timedependent open systems  8.3.4 NonHermitian quantum mechanical theory of high order harmonic generation  8.3.5 NonHermitian theory of above threshold ionization (ATI) spectra  8.4 Solutions to the exercises  8.5 Further reading  9 The selforthogonality phenomenon  9.1 The phenomenon of selforthogonality  9.1.1 The selforthogonal eigenvectors of nonHermitian matrices  9.2 On selforthogonality and the closure relations  9.2.1 On selforthogonality for complex potentials  9.3 Calculations of the radius of convergence of perturbational expansion of the eigenvalues in V0  9.4 The effect of selforthogonality on cexpectation values  9.5 Zero resonance contribution to the cross section  9.6 Geometric phases (Berry phases)  9.7 Concluding remarks  9.8 Solutions to the exercises  9.9 Further reading  10 The point where QM branches into two formalisms  10.1 Feshbach resonances  10.2 The point where QM branches into two formalisms  10.3 Concluding remarks  10.4 Solutions to the exercises  10.5 Further reading  Index 

The first book to present NHQM, useful to advanced graduate students and researchers in physics, chemistry and engineering 

Description based on publisher supplied metadata and other sources 

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries 
Link 
Print version: Moiseyev, Nimrod NonHermitian Quantum Mechanics
Cambridge : Cambridge University Press,c2011 9780521889728

Subject 
Quantum theory  Mathematics.;Hermitian structures.;Resonance.;Hermitian symmetric spaces


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