| Preface | p. xi |
| Different formulations of quantum mechanics | p. 1 |
| Hermitian operators: a brief review | p. 3 |
| Non-Hermitian potentials which support a continuous spectrum | p. 4 |
| Complex local potentials | p. 10 |
| Physical interpretation of complex expectation values | p. 11 |
| Concluding remarks | p. 12 |
| Solutions to the exercises | p. 13 |
| Further reading | p. 19 |
| Resonance phenomena in nature | p. 21 |
| Shape-type resonances | p. 21 |
| Feshbach-type resonances | p. 25 |
| Concluding remarks | p. 31 |
| Solutions to the exercises | p. 33 |
| Further reading | p. 39 |
| Resonances from Hermitian quantum-mechanical calculations | p. 41 |
| Resonances as metastable states | p. 41 |
| The poles of the S-matrix | p. 45 |
| Resonances from the spectra of density of states | p. 46 |
| Resonances from the asymptotes of continuum eigenfunctions | p. 50 |
| Resonances from the phase shifts | p. 54 |
| The scattering length | p. 57 |
| Resonances from stabilization calculations | p. 60 |
| Decay of resonance states | p. 64 |
| Real and complex poles of the scattering matrix from wavepacket propagation calculations | p. 70 |
| Concluding remarks | p. 71 |
| Solutions to the exercises | p. 72 |
| Further reading | p. 82 |
| Resonances from non-Hermitian quantum mechanical calculations | p. 84 |
| Resonances for a time-independent Hamiltonian | p. 86 |
| Transitions of bound states to anti-bound and resonance states | p. 91 |
| Bound, virtual and resonance states for a 1D potential | p. 95 |
| The mechanism of transition from a bound state to a resonance state | p. 97 |
| Concluding remarks on the physical and non-physical poles of the S-matrix | p. 101 |
| Resonances for a time-dependent Hamiltonian | p. 102 |
| Conservation of number of particles | p. 104 |
| Solutions to the exercises | p. 106 |
| Further reading | p. 115 |
| Square integrable resonance wavefunctions | p. 116 |
| The Zel'dovich transformation | p. 118 |
| The complex scaling transformation | p. 120 |
| The exterior scaling transformation | p. 127 |
| The smooth exterior scaling transformation | p. 129 |
| Dilation of the Hamiltonian matrix elements into the complex plane | p. 133 |
| Square integrability of field induced resonances | p. 136 |
| Partial widths from the tails of the wavefunctions | p. 142 |
| Concluding remarks | p. 147 |
| Solutions to the exercises | p. 149 |
| Further reading | p. 169 |
| Bi-orthogonal product (c-product) | p. 174 |
| The c-product | p. 174 |
| Completeness of the spectrum | p. 183 |
| Advantages of calculating survival probabilities by c-product | p. 186 |
| The c-product for non-Hermitian time-periodic Hamiltonians | p. 188 |
| The F-product for time propagated wavepackets | p. 190 |
| The F-product and the conservation of the number of particles | p. 195 |
| Concluding remarks | p. 196 |
| Solutions to the exercises | p. 197 |
| Further reading | p. 210 |
| The properties of the non-Hermitian Hamiltonian | p. 211 |
| The turn-over rule | p. 211 |
| The complex analog of the variational principle | p. 213 |
| The complex analogs of the virial and hypervirial theorem | p. 225 |
| The complex analog of the Hellmann-Feynman theorem | p. 226 |
| Cusps and 0-trajectories | p. 227 |
| Upper and lower bounds of the resonance positions and widths | p. 230 |
| Perturbation theory for non-Hermitian Hamiltonians | p. 235 |
| Concluding remarks | p. 237 |
| Solutions to the exercise | p. 238 |
| Further reading | p. 247 |
| Non-Hermitian scattering theory | p. 250 |
| Full collision processes for time-independent Systems | p. 254 |
| Half collision processes for time-independent Systems | p. 266 |
| Time-independent scattering theory for time-dependent Systems | p. 275 |
| Solutions to the exercises | p. 309 |
| Further reading | p. 318 |
| The self-orthogonality phenomenon | p. 323 |
| The phenomenon of self-orthogonality | p. 324 |
| On self-orthogonality and the closure relations | p. 334 |
| Calculations of the radius of convergence of perturbational expansion of the eigenvalues in V0 | p. 342 |
| The effect of self-orthogonality on c-expectation values | p. 343 |
| Zero resonance contribution to the cross section | p. 350 |
| Geometric phases (Berry phases) | p. 351 |
| Concluding remarks | p. 358 |
| Solutions to the exercises | p. 359 |
| Further reading | p. 373 |
| The point where QM branches into two formalisms | p. 375 |
| Feshbach resonances | p. 375 |
| The point where QM branches into two formalisms | p. 379 |
| Concluding remarks | p. 387 |
| Solutions to the exercises | p. 387 |
| Further reading | p. 391 |
| Index | p. 393 |
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