Rayleigh-Ritz variational method with suitable asymptotic behaviour

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• 作者：Francisco M. Fernández (1)
  Javier Garcia (1)
  
• 关键词：Rayleigh ; Ritz method ; asymptotic behaviour ; anharmonic oscillators ; rate of convergence ; orthogonal polynomial projection quantization
• 刊名：Central European Journal of Physics
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：12
• 期：8
• 页码：554-558
• 全文大小：1,167 KB
• 参考文献：1. C. N. Handy, D. Vrinceanu, J. Phys. A 46, 135202 (2013) CrossRef
  2. F. L. Pilar, Elementary Quantum Chemistry (McGraw-Hill, New York, 1968)
  3. F. M. Fernández, Cent. Eur. J. Phys. 11, 470 (2013). arXiv:1204.0229 [math-ph] CrossRef
  4. F. M. Fernández, Q. Ma, R. H. Tipping, Phys. Rev. A 39, 1605 (1989) CrossRef
  5. F. M. Fernández, Q. Ma, R. H. Tipping, Phys. Rev. A 40, 6149 (1989) CrossRef
  
• 作者单位：Francisco M. Fernández (1)
  Javier Garcia (1)
  
  1. INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica Diag, 113 y 64 (S/N), Sucursal 4, Casilla de Correo, 16 1900, La Plata, Argentina
  
• ISSN：1644-3608

文摘

This paper considers the Rayleigh-Ritz variational calculations with non-orthogonal basis sets that exhibit the correct asymptotic behaviour. This approach is illustrated by constructing suitable basis sets for one-dimensional models such as the two double-well oscillators recently considered by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.