On the uncertainty relation for angle variables

@article{Judge1964OnTU,  title={On the uncertainty relation for angle variables},  author={Darrell L. Judge},  journal={Il Nuovo Cimento (1955-1965)},  year={1964},  volume={31},  pages={332-340},  url={https://api.semanticscholar.org/CorpusID:120553526}}
  • D. Judge
  • Published16 January 1964
  • Physics
  • Il Nuovo Cimento (1955-1965)
SummaryThe uncertainty relation between the orbital angular momentum componentLz and the corresponding angleϕ is discussed. The uncertainty for an angle variable is defined. The formula ΔLz·Δϕ⩾1/2ħ, which is sometimes quoted, is shown to be incorrect, and an alternative relation, in full accord with the Heisenberg Uncertainty Principle, is derived.RiassuntoSi discute la relazione di indeterminazione fra la componenteLz del momento angolare orbitale ed il corrispondente angoloϕ. Si definisce l… 

43 Citations

Uncertainty relation with angle variables

SummaryAn extension of the recent work of Judge on establishing a correct uncertainty relation between orbital angular momentum and the corresponding angle variable is presented. The equation for the

On an uncertainty relation for angular variables

SummaryA proof is given of an uncertainty relation for angular variables, which has recently been conjectured by Judge.RiassuntoSi dà la dimostrazione di una relazione di indeterminazione per

Angular Momentum Uncertainty Relation and the Three-Dimensional Oscillator in the Coherent States

An angular momentum uncertainty relation is obtained in terms of sine and cosine operators that have a meaning even in a second-quantization formalism. For a threedimensional oscillator in coherent

Expectation values and uncertainties of radial and angular variables for a three-dimensional coherent oscillator

Calculates expectation values and uncertainties of the radial coordinate and momentum, and the azimuthal angle and angular momentum components for a three-dimensional harmonic oscillator in a

Minimum uncertainty states of angular momentum and angular position

The states of linear momentum that satisfy the equality in the Heisenberg uncertainty principle for position and momentum, that is the intelligent states, are also the states that minimize the

Sharp uncertainty relations for number and angle

We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the

Generalizing the Heisenberg uncertainty relation

The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) The resulting inequality is stronger because it includes the covariance between the two observables, and

Phase and Angle Variables in Quantum Mechanics

The quantum-mechanical description of phase and angle variables is reviewed, with emphasis on the proper mathematical description of these coordinates. The relations among the operators and state

Schwinger pair production and the extended uncertainty principle: can heuristic derivations be trusted?

    Y. Ong
    Physics
    The European Physical Journal C
  • 2020
The rate of Schwinger pair production due to an external electric field can be derived heuristically from the uncertainty principle. In the presence of a cosmological constant, it has been argued in

Gauge field, parity and uncertainty relation of quantum mechanics on S1

We consider the uncertainty relation between position and momentum of a particle on S 1 (a circle). Since S 1 is compact, the uncertainty of position must be bounded. Consideration on the uncertainty

3 References

Über eine neue Begründung der Quantenmechanik. II.

ZusammenfassungEs wird eine vereinfachte und verallgemeinerte Darstellung der in I. entwickelten Theorie gegeben. Eine Verallgemeinerung war insofern nötig, als dort nur die Theorie stetiger

Related Papers

Showing 1 through 3 of 0 Related Papers