Related papers: Generalized rotational hamiltonians from nonlinear…
The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational nuclear spectra is explicitly proved and a connection of this Hamiltonian to the formalisms of Amal'sky and…
Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants…
We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian $H$ and its…
The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N-dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained.…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
We show that similarity (or equivalent) transformations enable one to construct non-Hermitian operators with real spectrum. In this way we can also prove and generalize the results obtained by other authors by means of a gauge-like…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
We construct Lie algebras arising from commutators of the harmonic Hamiltonian and the perturbed anharmonic Hamiltonian. From there we form a very specific element of the associated Lie group and transform the unperturbed Hamiltonian into…
The algebra of fourvectors is described. The fourvectors are more appropriate than the Hamilton quaternions for its use in Physics and the sciences in general. The fourvectors embrace the 3D vectors in a natural form. It is shown the…
The relation between nonlinear algebras and linear ones is established. For one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to…
The study of the symmetry of Pais-Uhlenbeck oscillator initiated in [Nucl. Phys. B 885 (2014) 150] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
The simple, longitudinal, and transverse wobblers are systematically studied within the framework of collective Hamiltonian, where the collective potential and mass parameter included are obtained based on the tilted axis cranking approach.…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case.…
A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…