Spinless Salpeter equation as a simple matrix eigenvalue problem

Spinless Salpeter equation: Laguerre bounds on energy levels

“…[8]. These approaches include, among others, the development of elaborate numerical approximation methods [9,10,11] as well as the construction of effective Hamiltonians which, in spite of their apparently nonrelativistic form, incorporate relativistic effects by sophisticated momentum dependence of the involved parameters [12]. A lot of information on the solutions of the spinless Salpeter equation may even be gained by application of a relativistic virial theorem [13], most easily derived from a rather general "master virial theorem" [14].…”

MASS SPECTRA OF HEAVY QUARKONIA AND Bc DECAY CONSTANT FOR STATIC SCALAR-VECTOR INTERACTIONS WITH RELATIVISTIC KINEMATICS

“…Neglecting, furthermore, any reference to the spin degrees of freedom and restricting to positive energy solutions, one arrives at the SS equation, which is the correct tool to deal with the boundstate spectrum of qq, QQ and Qq or qQ (where q = u, d, s and Q = c, b, t) interacting via some effective potential with no spin dependence, i.e., spin-averaged data (SAD). This equation was solved analytically and then numerically for its bound-state energies using different techniques by many authors [3][4][5][6][7][8][9][10].…”

“…3 The prescription and the wave equation used are responsible for the deterioration of the fit parameters. The calculation and parameters are also model dependent as remarked in our earlier papers [10,31].…”

The spinless relativistic Yukawa problem

“…. , d−1, which allows us to localize eigenvalues by upper bounds of increasing tightness [13,14] for rising d. We find and have always found [15][16][17][18][19][20][21][22][23][24] it advantageous to span these finite-dimensional variational trial subspaces by a basis the representations of which are known analytically in both configuration and momentum space (related, of course, by Fourier transformation): in this case, the expectation values of H may be analytically given by evaluating those of T (p) in momentum space and those of V (x) in configuration space. By spherical symmetry, each basis vector factorizes into the product of a radial part and a spherical harmonic Y ℓm (Ω) for angular momentum ℓ and projection m depending on the solid angle Ω.…”