Book contents
- Frontmatter
- Contents
- Preface
- 1 Different formulations of quantum mechanics
- 2 Resonance phenomena in nature
- 3 Resonances from Hermitian quantum-mechanical calculations
- 4 Resonances from non-Hermitian quantum mechanical calculations
- 5 Square integrable resonance wavefunctions
- 6 Bi-orthogonal product (c-product)
- 7 The properties of the non-Hermitian Hamiltonian
- 8 Non-Hermitian scattering theory
- 9 The self-orthogonality phenomenon
- 10 The point where QM branches into two formalisms
- Index
2 - Resonance phenomena in nature
Published online by Cambridge University Press: 03 May 2011
- Frontmatter
- Contents
- Preface
- 1 Different formulations of quantum mechanics
- 2 Resonance phenomena in nature
- 3 Resonances from Hermitian quantum-mechanical calculations
- 4 Resonances from non-Hermitian quantum mechanical calculations
- 5 Square integrable resonance wavefunctions
- 6 Bi-orthogonal product (c-product)
- 7 The properties of the non-Hermitian Hamiltonian
- 8 Non-Hermitian scattering theory
- 9 The self-orthogonality phenomenon
- 10 The point where QM branches into two formalisms
- Index
Summary
Although the non-Hermitian formalism of quantum mechanics which is developed in this book is not limited to specific examples and is applicable to problems which are not necessarily quantum mechanical (such as problems which require the solution of the Maxwell equation rather than of the Schrödinger equation) we dedicate an entire chapter to resonance phenomena in nature since they are related to a broad range of subjects and fields in physics, chemistry, molecular biology and technology.
In this chapter we will introduce two different types of resonances, so called shape-type and Feshbach-type resonances, as they appear in different fields of science. The resonance phenomenon is associated with metastable states of a system that as time passes breaks into several subsystems. That is, even though the system has sufficient energy to break apart, this does not happen instantly but requires quite a long time with respect to the characteristic time scale of the system.
In Table 2.1 we give several examples of resonance phenomena, where we specify the decaying systems, the resulting subsystems, and classification in terms of shape and Feshbach resonances. (These concepts will be explained more formally later.)
Each of the listed systems has a typical time scale and in some of these cases the lifetime of the system is less than one nano-second while in other cases it takes more than several thousand years for the system to decay.
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- Non-Hermitian Quantum Mechanics , pp. 21 - 40Publisher: Cambridge University PressPrint publication year: 2011