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.
Forλ >0, the only real solution isα= 0, yieldingE= 1 2 + 3 4 λ, identical to first-order perturbation theory
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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.