Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2018 / Paper 2 / Section A(i) / 12 / iii / Solution

Since energy and angular frequency are related by $E=\hslash \omega$, the given eigenvalue relation yieldsWith $E_P=4.3\mathrm{eV}$,The ${\lambda }_i$ are dimensionless modal eigenvalues, not optical wavelengths despite the symbol. The same $\hslash$ multiplies both mode and bulk angular frequencies and cancels in the energy ratio. These are bare-core predictions of the stipulated lossless Drude model; adding a dielectric/metallic shell, interband response or damping changes the actual resonances.