Accurate numerical bounds for the spectral points of singular Sturm–Liouville problems over −∞
作者：
Highlights：
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摘要
The eigenvalues of singular Sturm–Liouville problems are calculated very accurately by obtaining rigorous upper and lower bounds. The singular problem over the unbounded domain (−∞,∞) is considered as the limiting case of an associated problem on the finite interval [−ℓ,ℓ]. It is then proved that the eigenvalues of the resulting regular systems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds converging monotonically to the required asymptotic eigenvalues. Numerical results for several quantum mechanical potentials illustrate that the eigenvalues can be calculated to an arbitrary accuracy, whenever the boundary parameter ℓ is in the neighborhood of some critical value, denoted by ℓcr.
论文关键词：81Q05,65L15,42C10,34L40,34B30,Sturm–Liouville problem,Schrödinger equation,Eigenvalue bound,Eigenvalue calculation,Eigenfunction expansion
论文评审过程：Received 21 August 1998, Revised 28 May 1999, Available online 14 February 2000.
论文官网地址：https://doi.org/10.1016/S0377-0427(99)00302-7
作者：
Highlights：
•
摘要
The eigenvalues of singular Sturm–Liouville problems are calculated very accurately by obtaining rigorous upper and lower bounds. The singular problem over the unbounded domain (−∞,∞) is considered as the limiting case of an associated problem on the finite interval [−ℓ,ℓ]. It is then proved that the eigenvalues of the resulting regular systems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds converging monotonically to the required asymptotic eigenvalues. Numerical results for several quantum mechanical potentials illustrate that the eigenvalues can be calculated to an arbitrary accuracy, whenever the boundary parameter ℓ is in the neighborhood of some critical value, denoted by ℓcr.
论文关键词：81Q05,65L15,42C10,34L40,34B30,Sturm–Liouville problem,Schrödinger equation,Eigenvalue bound,Eigenvalue calculation,Eigenfunction expansion
论文评审过程：Received 21 August 1998, Revised 28 May 1999, Available online 14 February 2000.
论文官网地址：https://doi.org/10.1016/S0377-0427(99)00302-7
