Energy bounds for the spinless Salpeter equation
نویسندگان
چکیده
منابع مشابه
Energy Bounds for the Spinless Salpeter Equation
We study the spectrum of the Salpeter Hamiltonian H = β √ m2 + p2 +V (r), where V (r) is an attractive central potential in three dimensions. If V (r) is a convex transformation of the Coulomb potential −1/r and a concave transformation of the harmonic-oscillator potential r, then upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form ...
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We study the eigenvalues En` of the Salpeter Hamiltonian H = β √ m2 + p2 +vr, v > 0, β > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula En` ≈ min r>0 { v(Pn`/r) 2 + β √ m2 + r2 } provides both upper and lower energy bounds for all the eigenvalues of the problem. PACS: 03.65.Ge, 03.65.Pm, 11.10.St En...
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We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schrödinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts are in L(R) for some p > n (n = 1 or 3). An extension to confining potentials, which are not in L(R), is also presented.
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The spinless Salpeter equation may be considered either as a standard approximation to the Bethe–Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a certain extent relativistic generalization of the costumary nonrelativistic Schrödinger formalism. Because of the presence of the rather difficult-to-handle square...
متن کاملTHE SPINLESS SALPETER EQUATION AND MESON DYNAMICS
Applying the variational method, the spinless reduced Bethe-Salpeter (RBS) equation is solved for the mesonic systems, and the mass spectra are obtained. The method is applied to the Hamiltonian with the Gaussian and hydrogen-type trial wave functions, and different potential models are examined. The results for the different potentials are in challenge in light mesons, while they are consisten...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2001
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1405848