ON THE COMPUTATION OF EIGENVALUE BOUNDS OF ANHARMONIC OSCILLATOR USING AN INTERMEDIATE PROBLEM METHOD

  • Lee, Gyou-Bong (Department of Applied Mathematics, Paichai University) ;
  • Lee, Ok-Ran (Department of Applied Mathematics, Paichai University)
  • Published : 2002.12.01

Abstract

We apply an Intermediate Problem Method to compute eigenvalues of an anharmonic oscillator. The method produces lower bounds to the eigenvalues while the Rayleigh-Ritz method yields upper bounds. We show the convergence rate of the Intermediate Problem Method is the same as the rate of the Rayleigh-Ritz method.

Keywords

References

  1. Symposium on Spectral Theory and Differential Problems VApproximation methods for eigenvalues of completely continuous symmetric operators N.Aronszajn
  2. Arch. Rat. Mech. Anal. v.10 TLower bounds to eigenvalues using operator decompositions of the form B*B N.Bazley;D.W.Fox
  3. Methods of mathematical physics v.1 R.Courant;D.Hilbert
  4. J. Korean Math. Sci. v.31 On lower bounds of eigenvalues for self adjoin operators G.Lee
  5. Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications A.Weinstein;W.Stenger