H. Taşeli, İ. M. Erhan and Ö. Uğur, An Eigenfunction Expansion for the Schrödinger Equation with Arbitrary Non-Central Potentials, Journal of Mathematical Chemistry, 32(4), pp. 323-338, (November 2002).

### Abstract

An eigenfunction expansion for the Schrödinger equation for a particle moving in an arbitrary non-central potential in the cylindrical polar coordinates is introduced, which reduces the partial differential equation to a system of coupled differential equations in the radial variable $$r$$. It is proved that such an orthogonal expansion of the wavefunction into the complete set of Chebyshev polynomials is uniformly convergent on any domain of $$(r, \theta)$$. As a benchmark application, the bound states calculations of the quartic oscillator show that both analytical and numerical implementations of the present method are quite satisfactory.

Keywords: two-dimensional Schrödinger equation, eigenfunction expansion, eigenvalue problems