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Results for “CENTRAL POTENTIAL”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

A Mathematical Method for Exact Analytical Solution of the Schroedinger Equation with Non-central Potential

In this paper, we have studied the Schroedinger equation with central and non-central potential. We have solved the Schroedinger equation in spherical coordinate analytically by using supersymmetric and shape invariance methods. Then we have found the radial and angular parts of wavefunction. Finally the energy eigenvalues of the Schroedinger equation with non-central potential are obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Relative Fisher information in some central potentials

Highlights: • Relative Fisher information in both r and p spaces is calculated analytically. • In case of central potentials, circular state of a given l, is selected as reference. • In hydrogenic system IR provides better result than that of I. • In case of oscillator potentials IR comments about change of bond strength with n{sub r}. - Abstract: Relative Fisher information (IR) was pursued for 1D quantum harmonic oscillator (QHO), 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both r and p spaces. In 1D case, the n=0 state is chosen as reference, whereas for a central potential, the respective circular (corresponding to lowest radial quantum number n{sub r}) state of a given l quantum number, is selected. Starting from their exact wave functions, expressions of IR in both r and p spaces are obtained in closed analytical forms in all these systems. For the 1D QHO, IR in r,p spaces increases linearly with n. For 3D QHO and PHP, it varies with single power of n{sub r} in both spaces. But, in H atom they depend on both principal (n) and azimuthal (l) quantum numbers. However, at a fixed l, IR initially advances with rise of n and then falls off; also for a given n, it always decreases with l.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Analysis of N-dimensional Klein–Gordon equation for hydrogen molecule in the non-central potential field

We investigate a complete normalized relativistic solutions for N-dimensional Hartmann potential and relativistic effects of non-central potential field for hydrogen molecule within the framework of asymptotic iteration approach. We also discuss in detail the influence of dimensions on the angular probability distribution of hydrogen molecule. N-dimensional bound state wavefunction solutions including angular and radial solutions are expressed in terms of the Jacobi and Laguerre polynomials, respectively. N-dimensional angular wavefunctions of hydrogen molecule were visualized with Matlab software. In hyperspherical coordinates, the recurrence relations between diagonal matrix elements have been derived for N-dimensional Hartmann potential in relativistic theory. We also obtain analytical expressions of diagonal matrix elements and the recurrence formula between off-diagonal matrix elements in N-dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Dynamics of zero-energy nonspreading non-Gaussian wave packets for a class of central potentials

Zero-energy wave packets, coherent states, are constructed in such a way that they retain their shape during the time evolution for a large class of central potentials. The packets are not of the Gaussian type with −r{sup 2} dependence but, instead, their shape is determined by −r{sup 1/(μ+1/2)} with −1/2<μ<1/2. A very close quantum–classical correspondence is also shown, i.e., the well localized states travel along suitable classical trajectories. -- Highlights: •Central potentials are considered. •Nonspreading, non-Gaussian wave packets are constructed. •Time evolution of the zero-energy packets is studied. •Quantum–classical correspondence is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Bound state solution of Dirac equation for Hulthen plus trigonometric Rosen Morse non-central potential using Romanovski polynomial

The bound state solutions of Dirac equation for Hulthen and trigonometric Rosen Morse non-central potential are obtained using finite Romanovski polynomials. The approximate relativistic energy spectrum and the radial wave functions which are given in terms of Romanovski polynomials are obtained from solution of radial Dirac equation. The angular wave functions and the orbital quantum number are found from angular Dirac equation solution. In non-relativistic limit, the relativistic energy spectrum reduces into non-relativistic energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Analytical solutions of a generalized non-central potential in N-dimensions

We present that N-dimensional non-relativistic wave equation for the generalized non-central potential with arbitrary angular momentum is analytically solvable in the hyperspherical coordinates. Asymptotic iteration method as a different approach is applied to obtain N-dimensional energy eigenvalues and the corresponding eigenfunctions. In hyperspherical coordinates, the wave function solutions are obtained in terms of hypergeometric functions and Jacobi polynomials. The bound states of quantum systems under consideration for some special cases, such as Hartmann and Makarov potentials, have been discussed in N-dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Non-universality of dark-matter halos: Cusps, cores, and the central potential

Dark-matter halos grown in cosmological simulations appear to have central Navarro–Frenk–White-like density cusps with mean values of dlogρ/dlogr≈−1, and some dispersion, which is generally parametrized by the varying index α in the Einasto density profile fitting function. Non-universality in profile shapes is also seen in observed galaxy clusters and possibly dwarf galaxies. Here we show that non-universality, at any given mass scale, is an intrinsic property of DARKexp, a theoretically derived model for collisionless self-gravitating systems. We demonstrate that DARKexp—which has only one shape parameter, ϕ{sub 0}—fits the dispersion in profile shapes of massive simulated halos as well as observed clusters very well. DARKexp also allows for cored dark-matter profiles, such as those found for dwarf spheroidal galaxies. We provide approximate analytical relations between DARKexp ϕ{sub 0}, Einasto α, or the central logarithmic slope in the Dehnen–Tremaine analytical γ-models. The range in halo parameters reflects a substantial variation in the binding energies per unit mass of dark-matter halos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Effect of a central barrier potential on asymmetry-induced transport in a coaxial Malmberg–Penning trap

Experiments are presented measuring the radial particle flux produced when a central barrier potential is applied to the central ring of a coaxial Malmberg-Penning trap at the same time as the voltages producing the main asymmetry potential $\phi_1(r)\cos{(kz)}\cos{(l\theta-\omega t)}$. When a negative DC voltage is applied to the entire central ring, the peak flux produced by the main asymmetry is reduced by a factor $e^{(V_{eff}/1.2)}$ where $V_{eff}$ is the effective applied potential in volts. This barrier potential also increases the frequency of this peak flux. When asymmetric $\pm$ voltages are applied to the two azimuthally-divided halves of the central ring, DC voltages increase the radial flux while AC voltages decrease it. It is shown that these asymmetric barrier voltages produce their own transport and that the resulting modification of the plasma may be a factor in changing the observed flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1990

Central-force potentials for interaction of rotationally and vibrationally excited molecules

A general and computationally efficient approach evaluating the central-force potentials for interaction of rotationally and vibrationally excited molecules and molecular ions is presented. Examples of numerical calculations are given for interactions of diatomic systems (H2, N2 and O2) in ground electronic states. The approach can be applied in a straightforward way to interactions of atoms and atomic ions with diatomic molecules in arbitrary rotational-vibrational states.

Kunc, Joseph A.↗
DOE OSTI2019

Properties of a potential energy matrix in oscillator basis

Matrix elements of potential energy are examined in detail. We consider a model problem — a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L{sup 2} basis (J-matrix) method for the quantum theory of scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Investigating the Rare Earth and Critical Mineral Potential of Central Appalachia

The Evolve Central Appalachia (Evolve CAPP) project team is investigating the rare earth and critical mineral resource potential of the Central Appalachian basin located in Virginia, West Virginia, Kentucky and Tennessee. Through a coalition of leading academic institutions, industry, research laboratories, expert consultants, and federal and state government agencies, the team is identifying opportunities in the region to supply the green and digital economy with responsibly sourced and sustainable critical minerals production and to spur downstream value-added industries that will stimulate economic growth in the CAPP region.

Bishop, Richard↗
DOE OSTI2011

Lambda-Nucleon Potential Calculated from Lattice QCD

We present our studies of Lambda-Nucleon ({Lambda}N) interaction by using lattice QCD. The equal-time Nambu-Bethe-Salpeter (NBS) amplitude of the lowest energy scattering state of a proton-{Lambda} system is calculated from lattice QCD. In this report, two different types of gauge configurations are employed: (i) Quenched QCD configurations at {beta} = 5.7 (a = 0.1416(9) fm) on a 32{sup 3}x48 lattice, whose spatial volume is (4.5 fm){sup 3}.(ii)2+1 flavor full QCD configurations generated by the PACS-CS collaboration at {beta} = 1.9 (a = 0.0907(13) fm) on a 32{sup 3}x64 lattice, whose spatial volume is (2.90 fm){sup 3}. The spin-singlet central potential is calculated from the NBS wave function for the spin J = 0 state, whereas the spin-triplet central potential as well as the tensor potential are deduced simultaneously from the NBS wave function for the spin J = 1 state by dividing it into the S-wave and the D-wave components.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

How Many Bursts Does It Take to Form a Core at the Center of a Galaxy?

We present a novel method for systematically assessing the impact of the central potential fluctuations associated with bursty outflows on the structures of dark matter halos for classical and ultrafaint dwarf (UFD) galaxies. Specifically, we use dark-matter-only simulations augmented with a manually added massive particle that modifies the central potential and approximately accounts for a centrally concentrated baryonic component. This approach enables precise control over the magnitude, frequency, and timing of rapid outflow events. We demonstrate that this method can reproduce the established result of core formation for systems that undergo multiple episodes of bursty outflows. In contrast, we also find that equivalent models involving only single (or a small number of) burst episodes do not form cores with the same efficacy. This is important because many UFDs in the local Universe are observed to have tightly constrained star formation histories that are best described by a single early burst of star formation. Using a suite of cosmological zoom-in simulations, we identify the regimes in which single bursts can and cannot form a cored density profile. Our results suggest that it may be difficult to form cores in UFD-mass systems with a single early burst, regardless of its magnitude.

cold dark matter↗
DOE OSTI2013

About a new family of coherent states for some SU(1,1) central field potentials

In this paper, we shall define a new family of coherent states which we shall call the 'mother coherent states,' bearing in mind the fact that these states are independent from any parameter (the Bargmann index, the rotational quantum number J, and so on). So, these coherent states are defined on the whole Hilbert space of the Fock basis vectors. The defined coherent states are of the Barut-Girardello kind, i.e., they are the eigenstates of the lowering operator. For these coherent states we shall calculate the expectation values of different quantum observables, the corresponding Mandel parameter, the Husimi's distribution function and also the P- function. Finally, we shall particularize the obtained results for the three-dimensional harmonic and pseudoharmonic oscillators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗