Forx= (z+∂ z)/ √ 2: ⟨x2⟩= 1 2 ⟨z∂z⟩+⟨z∂ z + 1⟩ = 1 2 2⟨z∂z⟩+ 1 = 1 2 1 + 4α2 1−4α 2 ,(A23) using⟨z 2⟩=⟨∂ 2 z ⟩= 0 and [∂ z, z] = 1

Expectation V alue of⟨x 4⟩for Generalized Gaussian (Squeezed-State) T rial F unctions Forψ(z) =e αz2 with realαand|α|< 1 2, the norm is ⟨ψ|ψ⟩= (1−4α 2)−1/2

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Rayleigh-Ritz Variational Method in The Complex Plane

quant-ph · 2026-02-27 · unverdicted · novelty 6.0

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.

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Rayleigh-Ritz Variational Method in The Complex Plane quant-ph · 2026-02-27 · unverdicted · none · ref 10
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.

Forx= (z+∂ z)/ √ 2: ⟨x2⟩= 1 2 ⟨z∂z⟩+⟨z∂ z + 1⟩ = 1 2 2⟨z∂z⟩+ 1 = 1 2 1 + 4α2 1−4α 2 ,(A23) using⟨z 2⟩=⟨∂ 2 z ⟩= 0 and [∂ z, z] = 1

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