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We study bound states of the two-dimensional Helmholtz equations withDirichlet boundary conditions in an open geometry given by two straight leadsof the same width which cross at an angle $\theta$. Such a four-terminaljunction with a tunable $\theta$ can realized experimentally if a right-anglestructure is filled by a ferrite. It is known that for $\theta=90^o$ there isone proper bound state and one eigenvalue embedded in the continuum. We showthat the number of eigenvalues becomes larger with increasing asymmetry and thebound-state energies are increasing as functions of $\theta$ in the interval$(0,90^o)$. Moreover, states which are sufficiently strongly bent exist inpairs with a small energy difference and opposite parities. Finally, we discusshow with increasing $\theta$ the bound states transform into the quasi-boundstates with a complex wave vector.Comment: 6 pages, 6 figure

Multiple bound states in scissor-shaped waveguides