Minimum uncertainty states for angular momentum operators

D. Rodríguez-Méndez, Shahen Hacyan, Rocío Jáuregui

Hossein Fakhri, M. Sayyah-Fard

V. Alan Kostelecký, Bogdan Tudose

Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized expectation values of the conjugate momentum. This implies, for example, that the mean angular momentum is quantized for any minimum-uncertainty state obtained from any uncertainty relation involving the angular-momentum operator and a conjugate coordinate. Experiments specifically seeking to create minimum-uncertainty states localized in angular coordinates therefore must produce packets with integer angular momentum. \textcopyright{} 1996 The American Physical Society.

Y. Ben-Aryeh

Minimum-uncertainty (MU) angular momentum states which are eigenstates of a nonunitary angular momentum displacement operator are found also to be eigenstates of a quasi-Hermitian Hamiltonian which has a certain metric with real eigenvalues. Various properties of these states are discussed. The relations between electromagnetic (EM) MU angular momentum states which have been proposed for improving the resolution in interferometers and the present theory are discussed.

Hong-Yi Fan

Based on the |λ> representation and the radius–phase description of an electron's orbit track in a uniform magnetic field, we introduce the phase operator and derive the minimum uncertainty states for the angular-momentum–phase uncertainty relation. The derivation makes full use of the newly constructed |l, r> representation which is the common eigenvector of the angular momentum Lz and the radius operator (K- - iΠ+)(K+ + iΠ-).