arXiv subjects
Publications and source records attributed to Rami Mehrem.
S-state Bound state solution to Schroedinger equation for an exponential potential is derived using the Mellin transform. This method is a new and an alternative to the usual method of reducing Schroedinegr equation to a Bessel differential equation. It involves solving a first order difference equation using iteration and induction.
In this paper, the integral $\pmatrix{λ_1 &λ_2 &λ_3\cr 0 &0 &0\cr}\, \int_0^\infty \, r^{λ_3+2}\, \exp{(-αr^2)}\, j_{λ_1}(k_1r) \,j_{λ_2}(k_2r) \,dr$, where $k_1$, $k_2$ and $α$ are positive, is evaluated analytically. The result is a finite sum over the modified spherical Bessel function of the first kind. This result will be useful for nuclear scattering calculations, where harmonic oscillator nuclear wavefunctions are used or when evaluating momentum space matrix elements for a Gaussian potential.
This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in nuclear scattering calculations, where an analytical result can provide an insight into the reaction mechanism. A technique is developed whereby an integral over several special functions which cannot be found in any standard integral table can be broken down into integrals that have existing analytical solutions