• Corpus ID: 246015659

Time Operators of Harmonic Oscillators and Their Representations I

@inproceedings{Hiroshima2022TimeOO,
  title={Time Operators of Harmonic Oscillators and Their Representations I},
  author={Fumio Hiroshima and Noriaki Teranishi},
  year={2022}
}
A time operator ˆ T ε of the one-dimensional harmonic oscillator ˆ h ε = 1 2( p 2 + εq 2 ) is rigorously constructed. It is formally expressed as ˆ T ε = 1 2 1 √ ε (arctan √ ε ˆ t + arctan √ ε ˆ t ∗ ) with ˆ t = p − 1 q . It is shown that the canonical commutation relation [ h ε , ˆ T ε ] = − i 1l holds true on a dense domain in the sense of sesqui-linear form, and the limit of ˆ T ε as ε → 0 is shown. Finally a matrix representation of ˆ T ε and its analytic continuation are given. 

References

SHOWING 1-10 OF 50 REFERENCES

Ultra-Weak Time Operators of Schrödinger Operators

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A Note on Time Operators

We construct a time operator of a self-adjoint operator H with finite dimensional CCR-domain. As corollaries, we show that there exists a time operator of H with infinite dimensional CCR-domain.

Quantum mechanical phase and time operator

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Continuous Hahn polynomials and the Heisenberg algebra

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Canonical conjugate momentum of discrete label operators in quantum mechanics I: formalism

We discuss the inadequacy of the standard definition of canonical conjugation for a quantum operator having adiscrete spectrum. A different definition is proposed, based on the analogy