Numerical Analysis of the Spectral Properties of Coupled Oscillator Schrödinger Operators. II. Two-Coupled Anharmonic Oscillators

We describe a simple method for the computation of many of the lowest eigenvalues and eigenfunctions of a two-coupled anharmonic oscillator approximation to the $:\phi ^4 :_2 $ quantum field theory [Int. J. Engrg. Sci., 18 (1980), pp. 341-349]. The method involves the diagonalization of effectively...

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Veröffentlicht in:SIAM journal on numerical analysis 1982-02, Vol.19 (1), p.126-141
Hauptverfasser: Isaacson, D., Isaacson, E. L., Marchesin, D., Paes-Leme, P. J.
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Sprache:eng
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Zusammenfassung:We describe a simple method for the computation of many of the lowest eigenvalues and eigenfunctions of a two-coupled anharmonic oscillator approximation to the $:\phi ^4 :_2 $ quantum field theory [Int. J. Engrg. Sci., 18 (1980), pp. 341-349]. The method involves the diagonalization of effectively sparse matrices. We prove that the eigenvalues and eigenvectors of the matrices converge to those of the operator faster than any inverse power of the size of the matrices. We give an error analysis of the method which includes the computation of rigorous bounds for the eigenvalues and eigenfunctions. The error analysis suggests that the rate of convergence is actually exponentially fast. We conjecture why this is the case.
ISSN:0036-1429
1095-7170
DOI:10.1137/0719006