Lambda‐Nucleon Interaction

Quarkonium bound-state problem in momentum space revisited

“…Admittedly, the problem is not new but our incentive here is to examine the effectiveness of the semi-spectral approach in solving strongly singular integral equations. Since the latter topic was beyond the scope of [1], this work may be regarded as an immediate continuation of the previous paper.…”

“…The above formula holds because the wave function φ ℓ (k ′ ) vanishes when k ′ tends to either of the integration end points. The resulting Cauchy principal value integral in (13) can be computed by using the dedicated Chebyshev quadrature given in [1]. Nevertheless, the lowering of the order of the pole outlined above has its price and in the integral on the right hand side of (13) the derivative of the unknown wave function will appear.…”

“…In contrast with the previous case, log |t − τ | singularity is integrable and the dedicated weighting functions Ω i (τ ) do exist even when τ coincides with either of the integration end-points. For explicit analytic expressions for all of the weighting functions introduced above the reader is referred to [1].…”

“…In a recent work [1] we have advocated the Chebyshev semi-spectral method demonstrating its efficiency in solving some typical differential and integral equations emerging in quantum mechanics. The present paper is in the same vein but here we wish to focus our attention solely on the heavy quarkonium momentum space bound-state problem.…”

“…In consequence, the expansion coefficients and the function values taken at the mesh-points are connected by a linear relation (cf. [1]). Thus, put in a nut-shell, the underlying idea is to solve the integral equation exactly on the Chebyshev mesh and, subsequently, interpolate by means of a high degree polynomial.…”