  The Tomasch effect (TE) is due to quasiparticle interference (QPI) as induced
by a nonuniform superconducting order parameter, which results in oscillations
in the density of states (DOS) at energies above the superconducting gap.
Quantum confinement in nanoscale superconductors leads to an inhomogenerous
distribution of the Cooper-pair condensate, which we found triggers the
manifestation of a new TE. We investigate the electronic structure of the
nanoscale superconductors by solving the Bogoliubov-de Gennes (BdG) equations
self-consistently and obtain the TE determined by two types of processes,
involving two or three particle QPIs. Both types of QPIs result in additional
BCS-like Bogoliubov-quasiparticles and BCS-like energy gaps leading to
oscillations in the DOS and modulated wave patterns in the local density of
states. These effects are strongly related to the symmetries of the system. A
reduced $4 \times 4$ inter-subbands BdG Hamiltonian is established in order to
describe analytically the TE of two-QPIs. Our study is relevant to nanoscale
superconductors, either nanowires or thin films, Bose-Einsten condensates and
confined systems such as two-dimensional electron gas interface
superconductivity.
