Geometrical representation of the equations for solving quantum beat problems

Kenji Furuya, Yasuhiko Gondo

Research output: Contribution to journalArticle

Abstract

Equations for solving a quantum beat problem in a three-level system, which determine two complex variables of time dependence, are rewritten in terms of four real functions constructed from the two complex variables. The Minkowski space is reasonably introduced in order to represent the time evolution of the four real functions as the motion of a four-dimensional vector, though the equations are irrelevant to the special theory of relativity. It is found that the four-dimensional vector precesses around the zeroth axis on the cone which is constructed from all of the points whose norms are zero in the Minkowski space, and that the Euclidean norm of the vector decreases with the increase of time. Though the visualized motion of the vector is similar to those in the well-known magnetic resonance precession model, the picture obtained from the equations for quantum beats cannot be connected with such a phenomenon as photon echo.

Original languageEnglish
Pages (from-to)4387-4393
Number of pages7
JournalThe Journal of Chemical Physics
Volume92
Issue number7
DOIs
Publication statusPublished - Jan 1 1990

Fingerprint

synchronism
complex variables
Minkowski space
norms
Relativity
Magnetic resonance
precession
time dependence
magnetic resonance
Cones
relativity
echoes
cones
Photons
photons

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Geometrical representation of the equations for solving quantum beat problems. / Furuya, Kenji; Gondo, Yasuhiko.

In: The Journal of Chemical Physics, Vol. 92, No. 7, 01.01.1990, p. 4387-4393.

Research output: Contribution to journalArticle

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