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<p>Time operators associated with an abstract semi-bounded self-adjoint operator <i>H</i> possessing a purely discrete spectrum are considered. The existence of a bounded self-adjoint time operator <i>T</i> for such an operator <i>H</i> is known as the Galapon time operator. In this paper, we construct a self-adjoint but <i>unbounded</i> time operator <i>T</i> for <i>H</i> with a dense CCR-domain, thereby extending the framework beyond the bounded setting.</p>

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Self-adjointness of unbounded time operators

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Fumio Hiroshima,
  • Noriaki Teranishi

摘要

Time operators associated with an abstract semi-bounded self-adjoint operator H possessing a purely discrete spectrum are considered. The existence of a bounded self-adjoint time operator T for such an operator H is known as the Galapon time operator. In this paper, we construct a self-adjoint but unbounded time operator T for H with a dense CCR-domain, thereby extending the framework beyond the bounded setting.