Book contents
- Frontmatter
- Contents
- Foreword by Claude Cohen-Tannoudji
- Preface
- Table of units and physical constants
- 1 Introduction
- 2 The mathematics of quantum mechanics I: finite dimension
- 3 Polarization: photons and spin-1/2 particles
- 4 Postulates of quantum physics
- 5 Systems with a finite number of levels
- 6 Entangled states
- 7 Mathematics of quantum mechanics II: infinite dimension
- 8 Symmetries in quantum physics
- 9 Wave mechanics
- 10 Angular momentum
- 11 The harmonic oscillator
- 12 Elementary scattering theory
- 13 Identical particles
- 14 Atomic physics
- 15 Open quantum systems
- Appendix A The Wigner theorem and time reversal
- Appendix B Measurement and decoherence
- Appendix C The Wigner–Weisskopf method
- References
- Index
Appendix C - The Wigner–Weisskopf method
Published online by Cambridge University Press: 05 January 2013
- Frontmatter
- Contents
- Foreword by Claude Cohen-Tannoudji
- Preface
- Table of units and physical constants
- 1 Introduction
- 2 The mathematics of quantum mechanics I: finite dimension
- 3 Polarization: photons and spin-1/2 particles
- 4 Postulates of quantum physics
- 5 Systems with a finite number of levels
- 6 Entangled states
- 7 Mathematics of quantum mechanics II: infinite dimension
- 8 Symmetries in quantum physics
- 9 Wave mechanics
- 10 Angular momentum
- 11 The harmonic oscillator
- 12 Elementary scattering theory
- 13 Identical particles
- 14 Atomic physics
- 15 Open quantum systems
- Appendix A The Wigner theorem and time reversal
- Appendix B Measurement and decoherence
- Appendix C The Wigner–Weisskopf method
- References
- Index
Summary
The derivation of the Fermi Golden Rule in Section 9.6.3 is limited to sufficiently short times t ≪ τ2, and the exponential decay law (9.171) cannot be justified using only the arguments of that section. A method due to Wigner and Weisskopf permits this law to be justified for long times with the help of another approximation scheme. Let us consider the following situation. A state of an isolated system a of energy Ea decays to a continuum of states b of energy Eb. Examples of such a situation are the de-excitation of an excited state of an atom, a molecule, a nucleus, and so on with the emission of a photon, or the decay of an elementary particle. The states of energy Ea and Eb are the eigenstates of a Hamiltonian H(0):
and a time-independent perturbation W is responsible for the transition a → b; in the case of spontaneous photon emission, W is given by (14.58). The states a and b are not stationary states of the total time-independent Hamiltonian H = H(0) + W. We can assume that the diagonal matrix elements of W are zero: Waa = Wbb = 0 and we use |ψ(t)〉 to denote the state vector of the system, the initial state being |ψ(t = 0)〉 = |a〉.
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- Information
- Quantum Physics , pp. 573 - 577Publisher: Cambridge University PressPrint publication year: 2006