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Self-adjoint phase operator

A. L. Alimov, E. V. Damaskinskii

Theoretical and Mathematical PhysicsJan 1, 19795 citations

Number-difference-phase uncertainty relation for NFM operational quantum phase description

Hong-Yi Fan, Min Xiao

Physics Letters AMar 1, 199713 citations

Self-adjoint Momentum Operator for a Particle Confined in a Multi-Dimensional Cavity

A. Mariani, U.‐J. Wiese

Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the momentum vector do not commute with each other unless very special conditions are met. As such, momentum measurements should be considered one direction at a time. We also extend other results, such as the Ehrenfest theorem and the interpretation of the Heisenberg uncertainty relation to higher dimensions.Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the momentum vector do not commute with each other unless very special conditions are met. As such, momentum measurements should be considered one direction at a time. We also extend other results, such as the Ehrenfest theorem and the interpretation of the Heisenberg uncertainty relation to higher dimensions.

arXiv:2309.07818Sep 14, 20230 citations

Self-adjoint momentum operator for a particle confined in a multi-dimensional cavity

A. Mariani, U.‐J. Wiese

Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the momentum vector do not commute with each other unless very special conditions are met. As such, momentum measurements should be considered one direction at a time. We also extend other results, such as the Ehrenfest theorem and the interpretation of the Heisenberg uncertainty relation to higher dimensions.Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the momentum vector do not commute with each other unless very special conditions are met. As such, momentum measurements should be considered one direction at a time. We also extend other results, such as the Ehrenfest theorem and the interpretation of the Heisenberg uncertainty relation to higher dimensions.

Journal of Mathematical PhysicsApr 1, 20243 citations

Self-adjoint extensions of phase and time operators (4 pages)

F. C. Khanna, Gilad Gour

Physical Review AJan 1, 20040 citations

Uncertainty on the Spiral: The Real and Imaginary Parts of the Quantum Exponent

Nicholas Archer Sanders

Quantum mechanics carries two uncertainty relations usually taught as one. This paper reads them as the real and imaginary parts of a single complex exponent e^(λ+i)θ. Position–momentum (ΔxΔp ≥ ℏ/2) is an i-phenomenon — Fourier conjugacy, substance-independent, importing ℏ/2 without deriving it; the slogan that uncertainty is "the equation of state of the atomic realm" is named and refused. Energy–time is different: not a conjugate-operator relation (t is not an operator; Pauli) but lifetime–linewidth, ΔE ≈ ℏΓ, the complex energy E₀ − iΓ/2 of Gamow and Weisskopf–Wigner — the inward λ-drain at the atomic floor of the nesting ladder, with Γ = −2ωλ from Entropy on the Spiral. This is the real equation of state the exponent discloses: a relation carrying a measurable rate. The framework is then stress-tested where most exposed — number–phase uncertainty against the absence of a self-adjoint phase operator (Dirac; Susskind–Glogower; Pegg–Barnett) — and the result is logged as a wall, not rescued. One organizing arrangement, one logged obstruction, no new number. The parent cosmology's falsification is reprinted.Quantum mechanics carries two uncertainty relations usually taught as one. This paper reads them as the real and imaginary parts of a single complex exponent e^(λ+i)θ. Position–momentum (ΔxΔp ≥ ℏ/2) is an i-phenomenon — Fourier conjugacy, substance-independent, importing ℏ/2 without deriving it; the slogan that uncertainty is "the equation of state of the atomic realm" is named and refused. Energy–time is different: not a conjugate-operator relation (t is not an operator; Pauli) but lifetime–linewidth, ΔE ≈ ℏΓ, the complex energy E₀ − iΓ/2 of Gamow and Weisskopf–Wigner — the inward λ-drain at the atomic floor of the nesting ladder, with Γ = −2ωλ from Entropy on the Spiral. This is the real equation of state the exponent discloses: a relation carrying a measurable rate. The framework is then stress-tested where most exposed — number–phase uncertainty against the absence of a self-adjoint phase operator (Dirac; Susskind–Glogower; Pegg–Barnett) — and the result is logged as a wall, not rescued. One organizing arrangement, one logged obstruction, no new number. The parent cosmology's falsification is reprinted.

Jul 2, 20268 citations

Self-adjoint Phase Difference Operator and Its Uncertainty Relation with Number Difference Operator

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