### Abstract

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 uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the constrained minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the constrained minimum uncertainty product states for the angular case by means of instructive approximations, a numerical iterative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.

Language | English |
---|---|

Pages | - |

Number of pages | 20 |

Journal | New Journal of Physics |

Volume | 7 |

DOIs | |

Publication status | Published - 17 Feb 2005 |

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### Keywords

- light
- linear momentum
- angular momentum
- angular position

### Cite this

*New Journal of Physics*,

*7*, -. https://doi.org/10.1088/1367-2630/7/1/062

}

*New Journal of Physics*, vol. 7, pp. -. https://doi.org/10.1088/1367-2630/7/1/062

**Minimum uncertainty states of angular momentum and angular position.** / Pegg, D T ; Barnett, S M ; Zambrini, R ; Franke-Arnold, S ; Padgett, M .

Research output: Contribution to journal › Article

TY - JOUR

T1 - Minimum uncertainty states of angular momentum and angular position

AU - Pegg, D T

AU - Barnett, S M

AU - Zambrini, R

AU - Franke-Arnold, S

AU - Padgett, M

PY - 2005/2/17

Y1 - 2005/2/17

N2 - 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 uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the constrained minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the constrained minimum uncertainty product states for the angular case by means of instructive approximations, a numerical iterative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.

AB - 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 uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the constrained minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the constrained minimum uncertainty product states for the angular case by means of instructive approximations, a numerical iterative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.

KW - light

KW - linear momentum

KW - angular momentum

KW - angular position

U2 - 10.1088/1367-2630/7/1/062

DO - 10.1088/1367-2630/7/1/062

M3 - Article

VL - 7

SP - -

JO - New Journal of Physics

T2 - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

ER -