Rayleigh-Ritz calculations in Segal-Bargmann space recover the exact harmonic-oscillator ground state and yield perturbative energy expansions for the quartic anharmonic oscillator via adaptive Gaussian trial functions.
The discriminant is ∆ = 36λ2 − 4 27 = 4 9λ2 − 1 27 ,(A32) so u3, v3 = 3λ± q 9λ2 − 1 27 .(A33) Taking real cube roots gives αopt = 3 r 3λ+ q 9λ2 − 1 27 + 3 r 3λ− q 9λ2 − 1 27 .(A34)
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Rayleigh-Ritz Variational Method in The Complex Plane
Rayleigh-Ritz calculations in Segal-Bargmann space recover the exact harmonic-oscillator ground state and yield perturbative energy expansions for the quartic anharmonic oscillator via adaptive Gaussian trial functions.