## Abstract

The rigged Hilbert space formalism of quantum mechanics provides a framework in which one can identify resonance states and obtain the typical exponential decay law. However, there remain questions of the interpretation and extraction of physical information through the calculation of expectation values of observables. The Lax-Phillips scattering theory provides a mathematical construction in which resonances are assigned with states in a Hilbert space, thus no such difficulties arise. The original Lax-Phillips structure is inapplicable within standard nonrelativistic quantum theory. Through the powerful theory of H^{p} spaces certain relations between the two theories are uncovered, which suggest that a search for a "unifying" framework might prove useful.

Original language | English |
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Pages (from-to) | 2285-2315 |

Number of pages | 31 |

Journal | International Journal of Theoretical Physics |

Volume | 42 |

Issue number | 10 |

DOIs | |

State | Published - 1 Oct 2003 |

Externally published | Yes |

## Keywords

- H spaces
- Lax-Phillips theory
- Resonance
- Rigged Hilbert space
- Semigroup evolution

## ASJC Scopus subject areas

- Mathematics (all)
- Physics and Astronomy (miscellaneous)