Comment on “On the energy levels of a finite square-well potential” [J. Math. Phys. 41, 4551 (2000)]

levels of the finite square-well potential, derived using the solution of the Riemann‐Hilbert boundary problem from the theory of analytic functions. The authors developed an asymptotic expansion for the energy levels E( p, k) in the limit of large p @where p5A2mV0L/(2\), m is the particle mass, V0 is the potential depth, L is the length of the finite well, and k is the quantum number#, and showed that the finite-well energy levels are approximately equal to those of an infinitely deep square well of length L8.L. In this comment, we correct an error in this asymptotic expansion @specifically in Ref. 1, Eq. ~28!# and point out that the connection between a finite well and a longer infinite well has been noted previously by other researchers. Paul and Nkemzi calculated @in Ref. 1, Eqs. ~25! and ~27!# that in the limit of large p, the quantized values of z5iA(V0 /E)21 take on the asymptotic form z p,k5pik~21! k S 1 4p 2 1 3p 2 2 2~ p11! p 2 k 2 D 1OS 1 p 3D . ~1! The energy levels of the finite square well are given in terms of z p, k by E~ p, k!5 V0