Mathematical analysis of the dimensional scaling technique for the Schrödinger equation with power-law potentials

DOI10.1063/1.3520359zbMath1314.81066OpenAlexW1980902985MaRDI QIDQ5255512

Chang-Shou Lin, Zhonghai Ding, Goong Chen

Publication date: 15 June 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://ntur.lib.ntu.edu.tw/bitstream/246246/238930/-1/84.pdf

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic expansions of solutions to PDEs (35C20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Many-body theory; quantum Hall effect (81V70) Molecular physics (81V55) Variational principles of physics (49S05)

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Cites Work

• Variational justification of the dimensional-scaling method in chemical physics: the H-atom
• Bifurcation for a semilinear elliptic equation on \({\mathbb{R}}^ N\) with radially symmetric coefficients
• Symétrie et compacité dans les espaces de Sobolev
• Existence of solitary waves in higher dimensions
• On the (non)compactness of the radial Sobolev spaces
• Analytic solution of the Schrödinger equation for the Coulomb-plus-linear potential. I. The wave functions
• Real Interpolation of Sobolev Spaces on Subdomains of Rn
• Visualization and dimensional scaling for some three-body problems in atomic and molecular quantum mechanics
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