Feynman integral treatment of the Bargmann potential

PTHA method based on path integral formulation is given for obtaining exact solution of the s states for the Bargmann potential where β and k are parameters. The exact energy spectrum and the normalised s-state eigenfunctions are obtained from the poles of the Green function and their residues, respectively. The results are compared with their of Schrödinger formalism, special cases are also discussed

Generalized Bertlmann–Martin inequalities and power-law potentials

PTHIn the three-dimensional Schrödinger equation, the generalized Bertlmann–Martin inequalities connect the moments of the ground state density to the energy differences between the lowest level of each angular momentum ℓ and the ground state. They are discussed in the case of the power-law potentials, as well as the lnr potential. Use is made of the derived moments to reconstruct the form factor F(q), i.e., the Fourier transform of the ground state density. Padé approximants are used to describe the high q behavior of the form factor when only a limited number of low order moments are known. The estimate of the ground state density at the origin is also discussed