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The Ψj(r,t) approximately factorize as R(r)ψj(θ,t)φ(z), where φ(z)=(mωz/π□)1/4exp(-mωz z2/2□), R(r)=(mωr/π□r2)1/4exp(-mωr[r-ρ]2/2□). This assumes √□/Mωr□ρ and ℓ□ρ/√□/Mωr, where □ℓ quantifies the maximum angular momentum (the latter optional simplification ensures the effective radial trapping potential, including a centrifugal term, can be considered identical for angular momenta up to ±□ℓ).
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/ 4 exp (- m ω r [r - ρ] 2 / 2 □). This assumes √ □ / M ω r □ ρ and ℓ □ ρ / √ □ / M ω r, where □ ℓ quantifies the maximum angular momentum (the latter optional simplification ensures the effective radial trapping potential, including a centrifugal term, can be considered identical for angular momenta up to ± □ ℓ).
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Where m is otherwise a known integer or half-integer value
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Where m is otherwise a known integer or half-integer value.
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77953749638
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This exact configuration is not strongly quasi-1D; it provides a useful basis for comparison, however, and we do not expect a quasi-1D mean field to be critical to the proposal's success
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This exact configuration is not strongly quasi-1D; it provides a useful basis for comparison, however, and we do not expect a quasi-1D mean field to be critical to the proposal's success.
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The vector notation is misleading, however, as the relative phase information between components is lost
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The vector notation is misleading, however, as the relative phase information between components is lost.
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Also ℓ=ρp/□ need not be integer valued
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Also ℓ = ρ p / □ need not be integer valued.
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