Few-Body Systems最新文献

A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude and phase as real quantities that together carry the same information that is contained in the complex wave function. Two main avenues for doing so go way back in the history of the subject and have been used both for scattering and bound states. A connection is made here to gauge transformations of electrodynamics where the advent of quantum mechanics and later quantum field theory showed the central role that local gauge transformations play in physics.

In this work, we investigate the Klein-Gordon and Dirac oscillators in (2+1) dimensions under the influence of a constant magnetic field, within the framework of energy-dependent noncommutative phase space. This space is characterized by two energy-dependent deformation parameters, (theta (E)) and (eta (E)), which modify the standard phase-space algebra through generalized commutation relations. By applying the Bopp shift method and using polar coordinates, we derive exact analytical solutions for both relativistic oscillators. The relativistic energy equations and corresponding wave functions are obtained explicitly in terms of confluent hypergeometric functions for the Klein-Gordon case and associated Laguerre functions for the Dirac case. We also analyze various limiting cases, including the commutative limit, the energy-independent NC case, and the non-relativistic regime. Our results show that the energy dependence of the noncommutative parameters leads to significant modifications in the spectral structure, potentially shedding light on quantum gravitational effects at high energies.

In this paper, we explore quantum dynamics of relativistic quantum oscillator field within the framework of generalized Klein-Gordon oscillator in the context of four-dimensional wormhole with a cosmic string. The considered space-time is an example of Morris-Thorne-type traversable wormhole with topological defect. We derive a radial second-order differential equation of the generalized Klein-Gordon oscillator equation and obtain analytical solution through special functions by choosing different potential functions. In this study, we consider two distinct functions: a Coulomb- and Cornell-like potential form and solve the differential equation. As particular case, we presented the ground state energy level and the corresponding wave function of quantum oscillator fields. In fact, it is shown that the wormhole throat radius and cosmic string influences the eigenvalue solution compared to flat space results. The presence of topological defect of cosmic string breaks the degeneracy of the spectra of energy.

In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator–which introduces reflection symmetry–we construct a deformed Schrödinger equation and obtain exact analytical solutions using the Pekeris approximation. The resulting energy spectrum and wavefunctions reveal how Dunkl parameters alter the effective potential and vibrational states. The model is applied to several diatomic molecules, including (hbox {H}_2), HCl, and (hbox {I}_2), illustrating the impact of symmetry deformation on energy spectra. We also compute thermodynamic functions including the partition function, free energy, internal energy, entropy, and specific heat. The analysis shows that the Dunkl deformation induces distinct thermal behavior and offers a tunable approach to molecular modeling. These results highlight the potential of the Dunkl formalism as a useful tool for extending conventional quantum models and for exploring symmetry-deformed systems in molecular physics and quantum thermodynamics.

The concept of grand angular momentum is widely used in the study of N-body problems quantum mechanically. Here, we applied it to a classical analysis of N-body problems. Utilizing the tree representation for Jacobi and hyperspherical coordinates, we found a decomposition of its magnitude into magnitudes of one-body angular momenta in three dimensions. We generalized some results from the two-body case and derived a general expression for the scattering angle in N-body problems.

In this work, we investigate the relativistic quantum motion of spin–zero scalar bosons via the Duffin–Kemmer–Petiau (DKP) equation with a position–dependent mass (PDM) system in the background of the topological defect space–time produced by a cosmic string. We determine the radial wave equation and obtain the exact analytical solutions of the wave equation for the linear and Cornell–type potential through the Bi–Confluent Heun differential equation. In fact, we have obtained the ground state energy for both potentials.

A method for the direct integration of the three-dimensional Faddeev equations with respect to the breakup T-matrix in momentum space for three-body systems with differing masses is presented. The Faddeev equations are explicitly formulated without imposing symmetry or antisymmetry requirements on the two-body t-matrices, thus accounting for mass differences between the three interacting particles. An algorithm for the algebraic determination of non-relativistic wave functions for three-body systems with arbitrary masses is given. Furthermore, it is directly demonstrated how the domain of logarithmic singularities in the integral kernels of the Faddeev equations is significantly altered by varying the masses of the interacting particles. The developed method for traversing logarithmic singularities is tested using the example of calculating the total cross sections for elastic neutron-deuteron scattering and breakup reaction.

We have done a systematic no-core shell-model study of (^{20-23})Na isotopes. The low-energy spectra of these sodium isotopes consisting of natural and un-natural parity states were reported, considering three realistic interactions: inside nonlocal outside Yukawa (INOY), charge-dependent Bonn 2000 (CDB2K), and the chiral next-to-next-to-next-to-leading order (N(^3)LO). We also present the mirror energy differences in the low-energy spectra of (|T_z|) = 1/2 mirror pair ((^{21})Na - (^{21})Ne). Apart from the energy spectra, we have also reported the electromagnetic transition strengths and moments. Finally, considering all three realistic interactions, we report the point-proton radii and neutron skin thicknesses.

In this work, the behavior of a lithium (Li) atom within a noncentral interacting endohedral fullerene under spherical confinement and in a quantum plasma environment is investigated. The relevant Schrödinger wave equation is solved using a hybrid approach that combines the tridiagonal matrix method and the asymptotic iteration method. Through this solution, the system’s energy levels, probability densities, dipole polarizabilities, and oscillator strengths are calculated. The changes in plasma density, plasma shielding effect, and endofullerene parameters significantly influence the dynamics of these fundamental properties. Specifically, the analysis of oscillator strengths reveals the strength of electromagnetic interactions during transitions within the system and details how these transitions are affected by plasma, endofullerene confinement, spherical confinement, and angular interactions. Changes in dipole polarizability illustrate how the atom evolves under the influence of these external factors, while differences in oscillator strengths play a critical role in understanding the efficiency of electronic transitions and the system’s interaction with electromagnetic waves. This work contributes to a better understanding of endohedral molecular systems in quantum plasma environments and provides a valuable foundation for modeling the properties of such systems. Moreover, as it serves as an important reference for broader investigations into the dynamics of noncentral endohedral fullerene and quantum plasma interactions at the atomic and molecular levels, it sheds light on future experimental and theoretical studies.

It is shown that the quantum Hamiltonian characterising a non-relativistic electron under the influence of an external spherical symmetric electromagnetic potential exhibits a supersymmetric structure. Both cases, spherical symmetric scalar potentials and spherical symmetric vector potentials are discussed in detail. The current approach, which includes the spin-(frac{1}{2}) degree of freedom, provides new insights to known models like the radial harmonic oscillator and the Coulomb problem. We also find a few new exactly solvable models, one of them exhibiting a new mixed type of shape invariance containing translation and scaling of potential parameters. The fundamental role as Witten parity played by the spin-orbit operator is high-lighted.