A spectral method for integration of the time-dependent Schrödinger equation in hyperspherical coordinates

We describe a spectral method for the direct numerical calculation of the time-dependent Schrödinger equation described in hyperspherical coordinates. The method is based on the split-step technique where the wavefunction is expanded in the appropriate eigenfunctions for the partial operators, making the time integration efficient, accurate and simple. The fast Fourier transform is applied to produce the expansion in the hyperradial direction, and a general hyperspherical harmonics transformation is applied to create an expansion in the angular directions. The latter transformation is set up by a combination of spherical harmonics and Jacobi polynomials. The method is ideal to describe correlated ionization dynamics of two-electron systems in strong fields and other phenomena where a hyperradial expansion is efficient. PACS numbers: 02.60.Cb, 02.70.Hm, 03.65.Ge