A spectral method for Schrodinger equations with smooth confinement potentials

作者：Gagelman Jerry; Yserentant Harry^*

来源：Numerische Mathematik, 2012, 122(2): 383-398.

DOI：10.1007/s00211-012-0458-8

We study the expansion of the eigenfunctions of Schrodinger operators with smooth confinement potentials in Hermite functions; confinement potentials are potentials that become unbounded at infinity. The key result is that such eigenfunctions and all their derivatives decay more rapidly than any exponential function under some mild growth conditions to the potential and its derivatives. Their expansion in Hermite functions converges therefore very fast, super-algebraically.

• 出版日期2012-10