 Odd resonance of a strongly repulsive symmetric double-delta potential

ID: odd-resonance-of-a-strongly-repulsive-symmetric-double-delta-potential

For

U_{0} a ≫ 1

, the lowest odd scattering resonance pole lies near the first odd mode trapped between the barriers:

k = \frac{π}{a} (1 - \frac{1}{U _{0} a} + O ((U_{0} a)^{- 2})) - i \frac{π ^{2}}{U _{0}^{2} a ^{3}} (1 + O ((U_{0} a)^{- 1}))

in its real part and to leading nonzero order in its imaginary part. Writing

E = ℏ^{2} k^{2} / (2 m) = E_{R} - i Γ/2

e^{- Γ t /ℏ}

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