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A particle in a one-dimensional delta-function potential and particle in abox are two well-known pedagogical examples; their combination, particle in abox with a delta-function potential V_\lambda(x)=\lambda\delta(x-x_0), too, hasbeen recently explored. We point out that it provides a unique example that issolvable in the weak (\lambda->0) and the strong (1/\lambda->0) couplinglimits. In either limit, the attractive and repulsive potentials lead toidentical spectra, with the possible exception of a single negative-energystate that is present when the potential is attractive. We numerically obtainthe spectra near the strong-coupling limit and discuss the consequences of thedegeneracy that arises when 1/|\lambda|=0.

Particle in a box with a delta-function potential: strong and weak coupling limits