2,506 research outputs found
An Algebraic Method for the Analytical Solutions of the Klein-Gordon equation for any angular momentum for some diatomic potentials
Analytical solutions of the Klein-Gordon equation are obtained by reducing
the radial part of the wave equation to a standard form of a second order
differential equation. Differential equations of this standard form are
solvable in terms of hypergeometric functions and we give an algebraic
formulation for the bound state wave functions and for the energy eigenvalues.
This formulation is applied for the solutions of the Klein-Gordon equation with
some diatomic potentials.Comment: 13 page
Approximate analytical solutions of Dirac Equation with spin and pseudo spin symmetries for the diatomic molecular potentials plus a tensor term with any angular momentum
Approximate analytical solutions of the Dirac equation are obtained for some
diatomic molecular potentials plus a tensor interaction with spin and
pseudospin symmetries with any angular momentum. We find the energy eigenvalue
equations in the closed form and the spinor wave functions by using an
algebraic method. We also perform numerical calculations for the
P\"oschl-Teller potential to show the effect of the tensor interaction. Our
results are consistent with ones obtained before
Analytical Solutions of Schr\"odinger Equation for the diatomic molecular potentials with any angular momentum
Analytical solutions of the Schrodinger equation are obtained for some
diatomic molecular potentials with any angular momentum. The energy eigenvalues
and wave functions are calculated exactly. The asymptotic form of the equation
is also considered. Algebraic method is used in the calculations.Comment: 21 page
Frequency-domain algorithm for the Lorenz-gauge gravitational self-force
State-of-the-art computations of the gravitational self-force (GSF) on
massive particles in black hole spacetimes involve numerical evolution of the
metric perturbation equations in the time-domain, which is computationally very
costly. We present here a new strategy, based on a frequency-domain treatment
of the perturbation equations, which offers considerable computational saving.
The essential ingredients of our method are (i) a Fourier-harmonic
decomposition of the Lorenz-gauge metric perturbation equations and a numerical
solution of the resulting coupled set of ordinary equations with suitable
boundary conditions; (ii) a generalized version of the method of extended
homogeneous solutions [Phys. Rev. D {\bf 78}, 084021 (2008)] used to circumvent
the Gibbs phenomenon that would otherwise hamper the convergence of the Fourier
mode-sum at the particle's location; and (iii) standard mode-sum
regularization, which finally yields the physical GSF as a sum over regularized
modal contributions. We present a working code that implements this strategy to
calculate the Lorenz-gauge GSF along eccentric geodesic orbits around a
Schwarzschild black hole. The code is far more efficient than existing
time-domain methods; the gain in computation speed (at a given precision) is
about an order of magnitude at an eccentricity of 0.2, and up to three orders
of magnitude for circular or nearly circular orbits. This increased efficiency
was crucial in enabling the recently reported calculation of the long-term
orbital evolution of an extreme mass ratio inspiral [Phys. Rev. D {\bf 85},
061501(R) (2012)]. Here we provide full technical details of our method to
complement the above report.Comment: 27 pages, 4 figure
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