4.1.1 Scaled Energy Dispersion Relation

For the sake of completeness the energy dispersion relation (q.v. (4.4) and (3.55)) after transformation to dimensionless units is given below:

$$\mathscr{E}\left(X\right)=\left\{\begin{array}{l r} \frac{X^{2}}{... ...{X^{2}+\zeta^{2}}+\zeta&\text{for}\enspace \zeta>1\enspace. \end{array} \right.$$ (4.16)