Application of the eigenvalue moment method to the quartic anharmonic double-well oscillator

Carlos R. Handy

doi:10.1103/PhysRevA.46.1663

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Application of the eigenvalue moment method to the quartic anharmonic double-well oscillator

Carlos R. Handy

Department of Physics, Clark Atlanta University, Atlanta, Georgia 30314
Center for Theoretical Studies of Physical Systems, Clark Atlanta University , Atlanta, Georgia 30314

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Phys. Rev. A 46, 1663 – Published 1 August, 1992

DOI: https://doi.org/10.1103/PhysRevA.46.1663

Abstract

The eigenvalue moment method (EMM) is a precise technique for generating converging lower and upper bounds to the low-lying eigenenergies of singular quantum Hamiltonians. We apply it to the quartic anharmonic double-well oscillator problem, $P^{2}$ - $Z^{2}$ $x^{2}$ + $x^{4}$ , recently studied by Saavedra and Buendia [Phys. Rev. A 42, 5073 (1990)]. In addition, we introduce important algorithmic modifications to the conventional EMM formulation, leading to more efficient applications.

References (12)

C. R. Handy and D. Bessis, Phys. Rev. Lett. 55, 931 (1985).
C. R. Handy et al., Phys. Rev. A 37, 4557 (1988).
C. R. Handy et al., Phys. Rev. Lett. 60, 253 (1988).
C. R. Handy et al., Phys. Rev. A 44, 1505 (1991).
F. Arias de Saavedra and E. Buendia, Phys. Rev. A 42, 5073 (1990).
C. R. Handy and P. Lee, J. Phys. A. 24, 1565 (1991).
J. A. Shohat and J. D. Tamarkin, The Problem of Moments (American Mathematical Society, Providence, RI, 1963).
A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961).
M. Ashbaugh and C. Sundberg (unpublished).
C. R. Handy and G. L Ndow, J. Phys. A: Math. Gen. 25, 2669 (1992).
D. Bessis et al., J. Phys. A 20, 419 (1987).
B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

[c1] C. R. Handy and D. Bessis, Phys. Rev. Lett. 55, 931 (1985).

[c2] C. R. Handy et al., Phys. Rev. A 37, 4557 (1988).

[c3] C. R. Handy et al., Phys. Rev. Lett. 60, 253 (1988).

[c4] C. R. Handy et al., Phys. Rev. A 44, 1505 (1991).

[c5] F. Arias de Saavedra and E. Buendia, Phys. Rev. A 42, 5073 (1990).

[c6] C. R. Handy and P. Lee, J. Phys. A. 24, 1565 (1991).

[c7] J. A. Shohat and J. D. Tamarkin, The Problem of Moments (American Mathematical Society, Providence, RI, 1963).

[c8] A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961).

[c9] M. Ashbaugh and C. Sundberg (unpublished).

[c10] C. R. Handy and G. L Ndow, J. Phys. A: Math. Gen. 25, 2669 (1992).

[c11] D. Bessis et al., J. Phys. A 20, 419 (1987).

[c12] B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

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Application of the eigenvalue moment method to the quartic anharmonic double-well oscillator

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