  In an attempt to regularize a previously known exactly solvable model [Yang
and Zhang, Eur. J. Phys. \textbf{40}, 035401 (2019)], we find yet another
exactly solvable toy model. The interesting point is that while the Hamiltonian
of the model is parameterized by a function $f(x)$ defined on $[0, \infty )$,
its spectrum depends only on the end values of $f$, i.e., $f(0)$ and $f(\infty
)$. This model can serve as a good exercise in quantum mechanics at the
undergraduate level.
