Is there a better way of representing stationary wave functions than basis expansion?

Abstract

AbstractWe extend our previously developed approach for finding the exact analytical form of ground state wave function of single‐electron Schrödinger equations to target arbitrary excited states of 1D model chemical systems of hydrogen atom and with soft Coulomb potential. Our representation of the wave functions is formally unified by a factorized formula involving a polynomial prefactor encoding the nodal information, a non‐integer power prefactor, and an exponentially decaying term modulated by a modulator function. We show that our method leads to faster energy convergence than the basis expansion method, and hence is a better way of representing the wave function. This conclusion is also validated in the real‐world .