Generalized pseudospectral methods with mappings for bound and resonance state problems

Several extensions of the pseudospectral method are made and applied to the solution of bound and resonance state problems. First, an algebraic mapping is introduced to remove the singularity and the domain truncation error common to Coulomb problems. In addition, the conventional procedure is modified, leading to a more desirable symmetric eigenvalue problem instead of an unsymmetric or generalized one. The simplicity, efficiency, and accuracy of the procedures are illustrated by solving the one-electron Dirac equation. Finally a new complex-scaling pseudospectral method is introduced for resonance state problems and applied to the determination of the complex resonance energies for an anharmonic oscillator.