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We extend the standard treatment of the asymmetric infinite square well toinclude solutions that have zero curvature over part of the well. This type ofsolution, both within the specific context of the asymmetric infinite squarewell and within the broader context of bound states of arbitrarypiecewise-constant potential energy functions, is not often discussed as partof quantum mechanics texts at any level. We begin by outlining the generalmathematical condition in one-dimensional time-independent quantum mechanicsfor a bound-state wave function to have zero curvature over an extended regionof space and still be a valid wave function. We then briefly review thestandard asymmetric infinite square well solutions, focusing on zero-curvaturesolutions as represented by energy eigenstates in position and momentum space.

More on the asymmetric infinite square well: energy eigenstates with zero curvature