2004/01/09 by Amlan K. Roy · 43 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Angular momentum #Boundary value problem #Discretization #Eigenvalues and eigenvectors #Excited state #Harmonic #Materials science #Mathematical analysis #Mathematics #Molecular Junctions and Nanostructures #Momentum (technical analysis) #Physics #Quantum mechanics #Range (aeronautics) #Schrödinger equation #Simple (philosophy) #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.1016/j.physleta.2003.12.037
published in Physics Letters A 321(4), 231-238 (Elsevier BV)
openalex publication_date 2004/01/09 · arxiv created 2013/07/04 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows nonuniform and optimal spatial discretization of the corresponding single-particle radial Schrödinger equation satisfying the Dirichlet boundary conditions leading to the standard diagonalization of the symmetric matrices. The present results for a large range of potential parameters are in excellent agreement with those from the other accurate methods available in the literature. The ground and excited states (both low as well as high angular momentum states) are obtained with equal ease and accuracy. Some new states including the higher excited states are reported here for the first time. This offers a simple, accurate and efficient method for the treatment of these and a wide variety of other singular potentials of physical and chemical interest in quantum mechanics.