An explicit construction is provided for embedding $n$ positive eigenvalues in the spectrum of a Schrödinger operator on the half-line with a Dirichlet boundary condition at the origin. The resulting potential is of von Neumann-Wigner type, but can be real-valued as well as complex-valued.
"Schrödinger operators with $n$ positive eigenvalues: an explicit construction involving complex-valued potentials." Proc. Japan Acad. Ser. A Math. Sci. 92 (1) 7 - 12, January 2016. https://doi.org/10.3792/pjaa.92.7