The generalized pseudospectral method has been established as a powerful numerical method to solve the three-dimensional atomic systems. In this work, we extend this method to the one-dimensional quantum systems in both free and confined situations, and focus especially on atoms with soft-core Coulomb interaction, a model that has been widely employed in the simulation of laser-atom interaction. The efficiency and robustness of the numerical method are thoroughly tested to ensure that the obtained eigenenergies are close to the working precision. Based on the highly accurate results, spectral properties of the one-dimensional atoms with soft-core Coulomb interaction are explored, including the asymptotic laws of eigenenergies, the quantum defects of bound states of different parities, and the variation and transition of eigenenergies and wave functions in different spatial confinements. These results complement the structural and spectral properties of one-dimensional atoms and promote further application of the low-dimensional models.

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• Electronic structure of atoms & molecules
• Mathematical physics
• 1-dimensional systems
• Atomic systems
• Numerical techniques
• Schroedinger equation