Ultra-Weak Time Operators of Schrödinger Operators

Asao Arai, Fumio Hiroshima

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)


    In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schrödinger operators HV with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions f: R→ R such that f(HV) has an ultra-weak time operator is found.

    Original languageEnglish
    Pages (from-to)2995-3033
    Number of pages39
    JournalAnnales Henri Poincare
    Issue number9
    Publication statusPublished - Sept 1 2017

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Nuclear and High Energy Physics
    • Mathematical Physics


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