Theory of Resonances

Feshbach resonances with large background scattering length: Interplay with open-channel resonances

“…Here ␦ nn Ј is the Kronecker delta, and the inner product is defined by means of analytic continuation in k of the proper bound-state eigensolutions to the resonance poles in the lower half of the complex k plane [49,50]. The normalization condition takes the form…”

“…The properties of the Mittag-Leffler expansion in terms of the Gamow resonance states have been extensively studied in the literature; see, e.g., Refs. [50][51][52][53]. We will therefore not give a derivation of the Mittag-Leffler expansion, but refer the reader to the literature.…”

−symmetric harmonic oscillators

“…Bound states acquire Im E = 0 and become re-interpreted as unstable resonances [17]. With quite a few important exceptions: It is already known for many years that certain non-hermitean Hamiltonians H = H + still do support perfectly stable bound states.…”

Supersymmetry Without Hermiticity

“…Similar analytic assumptions made in connection with quantized systems is not so unusual in the mathematically oriented literature [14]. Its appeal in physical applications is also undeniable and ranges from perturbative [15] and semiclassical methods and considerations [16] up to the practical computation of resonances [17]. In such a setting, the construction of representations of SUSY algebras encounters several new challenges.…”