A finite-dimensional representation of the quantum angular momentum operator (original) (raw)
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Alternative treatment of rotational quantum systems
Zeitschrift f�r Physik D Atoms, Molecules and Clusters, 1989
The method of the Hill determinant proves to be useful in treating purely rotating quantum systems. The rotational Stark effect in symmetric-top molecules and the internal rotation in molecules are discussed as illustrative examples. The procedure can be used either to obtain the energy eigenvalues for a given model potential or to built it from experimental data.
Alternative Description of Rigid Body Kinematics and Quantum Mechanical Angular Momenta
Geometry, Integrability and Quantization
In the present paper we investigate an alternative two-axes decomposition method for rotations that has been proposed in our earlier research. It is shown to provide a convenient parametrization for many important physical systems. As an example, the kinematics of a rotating rigid body is considered and a specific class of solutions to the Euler dynamical equations are obtained in the case of symmetric inertial ellipsoid. They turn out to be related to the Rabi oscillator in spin systems well known in quantum computation. The corresponding quantum mechanical angular momentum and Laplace operator are derived as well with the aid of infinitesimal variations. Curiously, the coefficients in this new representation happen to depend only on one of the angles, which simplifies the corresponding system of ODE's emerging from separation of variables. Some applications of the hyperbolic and complex analogues of this construction in quantum mechanics and relativity are considered in a different paper cited below.
Journal of Mathematical Physics, 1975
The purpose of this article is to present a detailed analysis on the quantum mechnical level of the canonical transformation between coordinate-momentum and number-phase descriptions for systems possessing an s i (2,R) dynamical algebra, specifically, the radial harmonic oscillator and pseudo-Coulomb systems. The former one includes the attractive and repulsive oscillators and the free particle, each with an additional "centrifugal" force. while the latter includes the bound, free and threshold states with an added "centrifugal" force. This is implemented as a unitary mappingcanonical transform-between the usual Hilbert space L 2 of quantum mechanics and a new set of Hilbert spaces on the circle whose coordinate has the meaning of a phase variable. Moreover, the UIR's D t of the universal covering group of S L (2,R) realized on the former space are mapped unitarily onto the latter.
Ju l 2 01 9 Quantum versus classical angular momentum
Angular momentum in classical mechanics is given by a vector. The plane perpendicular to this vector, in accordance to central field theory, determines the space in which particle motion takes place. No such simple picture exists in quantum mechanics. States of a particle in a central field are proportional to spherical harmonics which do not define any plane of motion. In the first part of the paper we discuss the angular distribution of particle position and compare it to the classical probabilistic approach. In the second part, the matter of addition of angular momenta is discussed. In classical mechanics this means addition of vectors while in quantum mechanics ClebschâȂŞGordan coefficients have to be used. We have found classical approximations to quantum coefficients and the limit of their applicability. This analysis gives a basis for the so called "vector addition model" used in some elementary textbooks on atomic physics. It can help to understand better the addition of angular momenta in quantum mechanics.
Quantum Rotational Spectra and Classical Rotors
International Journal of Modern Physics E, 2004
We consider the generalized rotor Hamiltonians capable of describing quantum systems invariant with respect to symmetry point-groups that go beyond the usual D2-symmetry of a tri-axial rotor. We discuss the canonical de-quantisation procedure to obtain the classical analogs of the original quantum Hamiltonians. Classical and quantum solutions to the Hamiltonians relevant in the nuclear physics applications are illustrated and compared using the 'usual' (D2) and an…
Angular-momentum projection of rotational model wave functions
Physics Letters B, 2000
Ž. Ž. It is known that angular momentum projection can be carried out analytically from highest weight states of l,0 SU 3 Ž irreps. It is shown here that they can also be projected analytically from deformed harmonic oscillator asymptotic Nilsson. model states and that these states become intrinsic states for rotational bands in the limit of large deformation. It is also Ž. shown that SU 3 is a good quasi-dynamical symmetry for a soft rotor with a large deformation.
Journal of Physics A: Mathematical and General, 2002
Following the discussion -in state space language -presented in a preceding paper, we work on the passage from the phase space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labeled) number of states. With that it is possible to relate an original Schwinger idea to the Pegg and Barnett approach to the phase problem. In phase space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian and angular coordinates, as limiting elements of the discrete phase space formalism. PACS: 03.65.-w, 03.65.Bz, 03.65.Ca