Solving the Coulomb Schrödinger equation in \(d= 2+1\) via sinc collocation (Q1815889)

Light cone quantization of quantum field theory is considered and the light cone radial Coulomb Schrödinger equation in 2+1 dimensions is solved. The power of the sinc collocation method used is demonstrated. The Coulomb Schrödinger equation is derived from the light cone quantization formalism. After transformations the singular Sturm-Liouville system \[ -f''(x)+\left[{4l^2-1\over 4x^2} +\ln x\right]f(x)=\lambda f(x) \] is obtained and solved by sinc collocation. A good convergence is attained.