ROVIBRATIONAL BOUND STATES OF THE Ar2Ne COMPLEX

2013 ◽  
Vol 12 (01) ◽  
pp. 1250107 ◽  
Author(s):  
BENHUI YANG ◽  
BILL POIRIER
Keyword(s):  
Quantum Dynamics ◽  
Bound States ◽  
Energy Levels ◽  
Effective Potentials ◽  
Spectral Transform ◽  
Physical Insight ◽  
Rovibrational States ◽  
Three Body ◽  
Massive Parallelization ◽  
Variable Representation

We report exact quantum dynamics calculations of the eigenstate energy levels for the bound rovibrational states of the Ar2Ne complex, across the range of J values for which such states are observed (J = 0–35). All calculations have been carried out using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform (PIST) methods, together with an effective massive parallelization scheme. The Ar2Ne energy levels were computed using a pair-wise Aziz potential plus a three-body correction, in Jacobi co-ordinates. Effective potentials for the radial co-ordinates are constructed, which reveal important physical insight into the two distinct dissociation pathways, Ar2Ne → NeAr + Ar and Ar2Ne → Ar2 + Ne . A calculation of the bound vibrational (J = 0) levels, computed using the Tang–Toennies potential, is also performed for comparison with results from the previous literature.

QUANTUM DYNAMICAL CALCULATION OF ALL ROVIBRATIONAL STATES OF HO2 FOR TOTAL ANGULAR MOMENTUM J = 0–10

2010 ◽  
Vol 09 (02) ◽  
pp. 435-469 ◽  
Author(s):  
WENWU CHEN ◽  
BILL POIRIER
Keyword(s):  
Angular Momentum ◽  
Quantum Dynamics ◽  
Bound States ◽  
Total Angular Momentum ◽  
Energy Levels ◽  
Rigid Rotor ◽  
Spectral Transform ◽  
Software Modules ◽  
Rovibrational States ◽  
Rotor Model

The energy levels and wavefunctions for all rovibrational bound states of HO2 are systematically computed, for all total angular momentum values J = 0–10. The calculations are performed using ScalIT, a suite of software modules designed to enable quantum dynamics and related calculations to be performed on massively parallel computing architectures. This is the first-ever application of ScalIT to a real (and very challenging) molecular application. The codes, and in particular, the algorithms (optimal separable basis, preconditioned inexact spectral transform, phase space optimized discrete variable representation basis) are so efficient that in fact, the entire calculation can be performed on a single CPU — although parallel scalability over a small number of CPUs is also evaluated, and found to be essentially perfect in this regime. For the lowest 11 vibrational states, the rotational levels for J = 0–10 fit fairly well to a rigid rotor model, with all vibrational-state-dependent rotational constants, B eff (v), close to values obtained from a previous calculation for J = 0 and 1 [J Chem Phys107:2705, 1997]. However, comparatively larger discrepancies with the rigid-rotor model are found at the higher J values, manifesting in the observed K-splitting (along the O–O bond) of rovibrational levels. This supports earlier work [J Chem Phys113:11055, 2000] suggesting that Coriolis coupling is quite important for this system.

Highly excited rovibrational states of small molecules

1990 ◽  
Vol 332 (1625) ◽  
pp. 329-341 ◽  
Keyword(s):  
First Principles ◽  
Energy Levels ◽  
Dipole Approximation ◽  
Rotational Spectrum ◽  
Discrete Variable Representation ◽  
Triatomic Molecules ◽  
Step Procedure ◽  
Variational Calculations ◽  
Rovibrational States ◽  
Variable Representation

The use of first principles variational calculations for the calculation of high-lying energy levels, wavefunctions and transition intensities for triatomic molecules is considered. Theoretical developments are considered, including the use of generalized internal coordinates, the use of a two-step procedure for rotationally excited systems and a finite element method known as the discrete variable representation. Illustrative calculations are presented including ones for H 2, LiCN and the Ar-N2 Van der Waals molecule. A first principles ‘rotational’ spectrum of H 2D+ is computed using states up to J = 30. The transition intensities in this spectrum are reproduced accurately in a frozen dipole approximation but are poorly represented by models that involve approximating the wavefunction.

scholarly journals Spin-0 scalar particle interacts with scalar potential in the presence of magnetic field and quantum flux under the effects of KKT in 5D cosmic string spacetime

2020 ◽  
pp. 2150004
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Magnetic Field ◽  
Quantum Dynamics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Klein Theory ◽  
Klein Gordon ◽  
Quantum Flux

In this paper, we study a relativistic quantum dynamics of spin-0 scalar particle interacts with scalar potential in the presence of a uniform magnetic field and quantum flux in background of Kaluza–Klein theory (KKT). We solve Klein–Gordon equation in the considered framework and analyze the relativistic analogue of the Aharonov–Bohm effect for bound states. We show that the energy levels depend on the global parameters characterizing the spacetime, scalar potential and the magnetic field which break their degeneracy.

Nonvariational and nonadiabatic calculations on the hydrogen molecular ion and its µ – isotopes

2002 ◽  
Vol 80 (11) ◽  
pp. 1423-1432 ◽  
Author(s):  
V Yakhontov ◽  
M Jungen
Keyword(s):  
Molecular Ions ◽  
Nuclear Motion ◽  
Mass Ratio ◽  
Internuclear Separation ◽  
Nonadiabatic Coupling ◽  
Effective Potentials ◽  
Continuum States ◽  
Variational Techniques ◽  
Rovibrational States ◽  
Three Body

A nonadiabatic, nonvariational, and computationally inexpensive scheme to describe bound and continuum states of three-body molecular ions, including µ –-mesonic ions, is proposed. The method relies on treating perturbatively the nonadiabatic coupling between the Born–Oppenheimer (BO) particle states and nuclear motion terms, such that the appropriate expansion parameter is the mass ratio of the lightest particle in the system to that of the heaviest one. In practice, the method requires solving, numerically, a system of coupled inhomogeneous Schrödinger equations with effective potentials that depend on the "internuclear" separation, R, and allow for the mixing of BO states because of nonadiabatic terms in the Hamiltonian. The utility of our approach is clearly evidenced by the results of the numerical calculations carried out for rovibrational states of several lowest J in the H+2 and (ppµ–) molecules. These demonstrate that nonadiabatic eigenenergies and eigenstates, both of the bound and scattering type, for ordinary as well as µ-mesonic molecules can be directly and quite accurately calculated from the same principles in the entire range of R, without making use of the variational techniques that more sophisticated studies of this kind are usually based on. PACS Nos.: 31.15Ar, 31.15Pf

scholarly journals Quantum states of a neutral massive fermion with an anomalous magnetic moment in an Aharonov–Casher field

2017 ◽  
Vol 32 (18) ◽  
pp. 1750111
Author(s):  
V. R. Khalilov
Keyword(s):  
Cross Sections ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Dynamics ◽  
Bound States ◽  
Scattering Amplitude ◽  
Energy Levels ◽  
Initial State ◽  
Massive Fermion ◽  
A Charge

The planar nonrelativistic quantum dynamics of a neutral massive fermion with an anomalous magnetic moment (AMM) in the electric field of infinitely long and thin thread with a charge density distributed uniformly along it (an Aharonov–Casher field) is examined. The relevant Hamiltonian is singular and requires additional specification of a one-parameter self-adjoint extension, which can be given in terms of physically acceptable boundary conditions. We find all possible self-adjoint Hamiltonians with an Aharonov–Casher field (ACF) by constructing the corresponding Hilbert space of square-integrable functions, including the [Formula: see text] region, for all their Hamiltonians. We determine the most relevant physical quantities, such as energy spectrum and wave functions and discuss their correspondence with those obtained by the physical regularization procedure. We show that energy levels of bound states are simple poles of the scattering amplitude. It is shown that the scattering amplitudes and cross-sections depend essentially on the initial-state spin of fermions.

THE ANALOGUE OF THE AHARONOV–BOHM EFFECT FOR BOUND STATES FOR NEUTRAL PARTICLES

2011 ◽  
Vol 26 (18) ◽  
pp. 1331-1341 ◽  
Author(s):  
KNUT BAKKE ◽  
C. FURTADO
Keyword(s):  
Bound States ◽  
Neutral Particle ◽  
Energy Levels ◽  
Quantum Ring ◽  
Persistent Currents ◽  
One Dimensional ◽  
Neutral Particles ◽  
Quantum Flux ◽  
Bohm Effect ◽  
Aharonov Bohm

We study the analogue of the Aharonov–Bohm effect for bound states for a neutral particle with a permanent magnetic dipole moment interacting with an external field. We consider a neutral particle confined to moving between two coaxial cylinders and show the dependence of the energy levels on the Aharonov-Casher quantum flux. Moreover, we show that the same flux dependence of the bound states can be found when the neutral particle is confined to a one-dimensional quantum ring and a quantum dot, and we also calculate the persistent currents in each case.

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

2021 ◽  
pp. 157-169
Author(s):  
G.A. Bayramova ◽  
Keyword(s):  
Analytical Solution ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Radial Wave ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

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