Lyapunov Operators

  • Lawrence HorwitzEmail author
  • Yosef Strauss
Part of the Mathematical Physics Studies book series (MPST)


In this chapter we discuss the construction of self-adjoint operators indicating the direction of time within the framework of standard quantum mechanics (Strauss 2011). Such operators will be referred to as Lyapunov operators. The particular construction of Lyapunov operators in this section will enable us to develop a formalism providing a good approximation to the Lax–Phillips theory for scattering problems involving Hamiltonians with semibounded spectra, as we do in Chap.  4. The construction of Lyapunov operators, moreover, has an intrinsic interest of its own.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Physics, Raymond and Beverly Sackler, Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael
  2. 2.Department of PhysicsBar-Ilan UniversityRamat GanIsrael
  3. 3.Department of PhysicsAriel UniversitySamariaIsrael
  4. 4.Department of MathematicsBen-Gurion University of the NegevBeér ShevaIsrael

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