### Abstract

We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over - ∞ < t < +∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t _{0}: t _{0} ≤ t < +∞, for which the mathematicians would choose t _{0} = 0,^{1} but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time t_{0}^{i} for an ensemble of individual quanta.

Original language | English (US) |
---|---|

Pages (from-to) | 14-26 |

Number of pages | 13 |

Journal | Journal of Russian Laser Research |

Volume | 35 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2014 |

Externally published | Yes |

### Fingerprint

### Keywords

- boundary conditions
- Hardy spaces
- time-asymmetric quantum mechanics

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Engineering (miscellaneous)

### Cite this

*Journal of Russian Laser Research*,

*35*(1), 14-26. https://doi.org/10.1007/s10946-014-9396-5

**Boundary Conditions for the Dynamical Equations of Quantum Mechanics.** / Bohm, Arno; Bui, H. V.; Kielanowski, P.

Research output: Contribution to journal › Article

*Journal of Russian Laser Research*, vol. 35, no. 1, pp. 14-26. https://doi.org/10.1007/s10946-014-9396-5

}

TY - JOUR

T1 - Boundary Conditions for the Dynamical Equations of Quantum Mechanics

AU - Bohm, Arno

AU - Bui, H. V.

AU - Kielanowski, P.

PY - 2014/1

Y1 - 2014/1

N2 - We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over - ∞ < t < +∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t 0: t 0 ≤ t < +∞, for which the mathematicians would choose t 0 = 0,1 but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time t0i for an ensemble of individual quanta.

AB - We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over - ∞ < t < +∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t 0: t 0 ≤ t < +∞, for which the mathematicians would choose t 0 = 0,1 but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time t0i for an ensemble of individual quanta.

KW - boundary conditions

KW - Hardy spaces

KW - time-asymmetric quantum mechanics

UR - http://www.scopus.com/inward/record.url?scp=84897580298&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897580298&partnerID=8YFLogxK

U2 - 10.1007/s10946-014-9396-5

DO - 10.1007/s10946-014-9396-5

M3 - Article

AN - SCOPUS:84897580298

VL - 35

SP - 14

EP - 26

JO - Journal of Russian Laser Research

JF - Journal of Russian Laser Research

SN - 1071-2836

IS - 1

ER -