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Quantum integrable systems related with group U(1,3) are considered. The explicit expressions of waves functions, Harish–Chandra c-functions and S-matrices are given.

Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrödinger equation to various exactly solvable sextic anharmonic oscillator and confining perturbed Coulomb models in D-dimensions. We show that the perturbed Coulomb problem with eigenvalue E can be transformed to a sextic anharmonic oscillator problem with eigenvalue . We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solutions of these potentials exist when their coupling parameters with k = D +2ℓ appearing in the wave equation satisfy certain constraints.

In this paper, we investigate the Duffin–Kemmer–Petiau (DKP) equation for spin-0 system of charge-free particles in the background of a flat class of Gödel-type spacetimes, and evaluate the individual energy levels and corresponding wave functions in detail.

We study universality in the data of the electroproduction of vector mesons, using as guideline the results of a unified nonperturbative approach which reproduces well the available experimental data. After the extraction of factors that are specific of each vector meson, we arrive at a reduced integrated elastic cross-section which is universal. Our analysis suggests a finite infrared behavior for the strong coupling constant.

In this paper, we study the relativistic quantum dynamics of spin-0 scalar charged particles with a magnetic quantum flux produced by topological defects in a rotating cosmic string space–time. We solve the Klein–Gordon equation subject to Coulomb-type scalar and vector potentials in the considered framework and obtain the energy eigenvalues and eigenfunctions and analyze the analogue effect to Aharonov–Bohm effect for bound states.

We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems with time-independent Hamiltonians. The mapping of dynamics can be performed in any dimension, for an arbitrary number of interacting particles and for any type of the scaling interaction potential. The exact solvability of a "dual" time-independent Hamiltonian automatically means the exact solvability of the original problem with model time-dependence.

We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schrödinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted harmonic oscillator. As a special case, we consider a generalized inverted oscillator with constant frequency and exponentially increasing mass.

There are two ways to choose the generating functions of the gauge transformations $T_D(\mathrm{\Phi })={({\mathrm{\Phi }}^{-1})}_x^{-1}\partial {\mathrm{\Phi }}^{-1}$ and $T_I(\mathrm{\Psi })={\mathrm{\Psi }}^{-1}{\partial }^{-1}{\mathrm{\Psi }}_x$, when dicussing the gauge transformations for the constrained modified KP hierarchy. The first is to select the (adjoint) eigenfunctions, while the second is the (adjoint) wave functions. In this paper, we will mainly discuss the gauge transformations obtained by the second method. The corresponding successive applications are considered. Also, we investigate the results of the gauge transformation derived through the union of these two methods.

The decay pattern of the low lying levels in the shape transitional nucleus ¹⁵⁰Sm is analyzed in terms of the quasi-vibrational and quasi-rotational collective model. The Dynamic Pairing plus quadrupole Model in the microscopic theory of the collective model is employed to predict extensive structure characteristics. The potential energy surface (PES), the spectroscopic factors and the E2, E0 transition rates from the DPPQ model are illustrated. Comparison is made with the predictions in the Interacting Boson Model (IBM-1). A correspondence is demonstrated of the effect of the control parameter in the two models on the calculated nuclear structure. The study of the wave functions of the two spin I = 2 excited states in IBM is carried out. The alternative view of an anharmonic vibrator and a soft rotor is discussed in terms of the E2 transition rates and other structural characteristics.

The problem of a spineless charged particle with a time-dependent decaying mass interacting with a Coulomb and an inverse quadratic potentials is considered. The Green’s function is explicitly evaluated. The energy levels as well as the wave functions for the bound states are exactly determined.

We have presented a particular direct method to solve time-dependent quantum problems within the framework of path integrals by using explicitly time-dependent transformations. We have applied it to the case of harmonic oscillator with time-dependent mass and frequency. Some examples have illustrated the method used. From their exact propagators, normalized solutions have been obtained.