Title: Quasimomentum of an elementary excitation for a system of point bosons with zero boundary conditions,
Abstract: As is known, an elementary excitation of a many-particle system with
boundaries is not characterized by a definite momentum. Here, we obtain the
formula for the quasimomentum of an elementary excitation for a one-dimensional
system of $N$ spinless point bosons with zero boundary conditions (BCs). We
also find that the dispersion law $E(p)$ of the system with zero BCs coincides
with that of a system with periodic BCs. The elementary excitations are defined
within a new approach proposed earlier by the author. This approach is
mathematically equivalent to the traditional approach by Lieb, but differs from
it by a simpler way of enumeration of excited states and leads to a single
dispersion law (instead of two ones in the Lieb's approach).