Extensions of Variational Methods, I : Super-Stationary Variational Method

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概要

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• Several methods to improve the degree of approximation for the stationary character in variational methods, are discussed. By selecting a set of trial functions as prescribed in the present paper, it is shown that we can construct quite generally a super-stationary expression for the quantity we wish to find. By "super-stationary" we mean that, the first, second and third variations of that expression vanish for any infinitesimal variations of trial functions. The examples to which this method is applied are : I). To find the eigenvalue in the eigenvalue-problems with discrete spectra only, (for example, to find the potential depth in the deuteron problem). II). To find the discrete eigenvalues for the problems with both discrete and continuous spectra, (for example, to find the energy level of the deuteron). III). To solve problems for continuous spectra by integral equations. IV). To solve problems for continuous spectra by differential equations. Also a method is mentioned for improving approximation of the stationary character in successive manner in each case and it is shown that a simple method for this improvement exists in the cases I)and II).

• 理論物理学刊行会の論文

著者

• Kikuta Takashi

  Department Of Physics Faculty Of Science University Of Tokyo

関連論文

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• Extensions of Variational Methods, II : Two Parameter Eigenvalue Problem for the Deuteron State
• Convergence of Iterative Methods
• Extensions of Variational Methods, I : Super-Stationary Variational Method

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