A didactically motivated reexamination of a particle’s quantum mechanics with square-well potentials

We address two questions regarding square-well potentials from a didactic perspective. The first question concerns whether or not the justification of standard priori omission potential’s vertical segments in analysis eigenvalue problem is licit. detour we follow to find out answer considers trapezoidal potential, includes solution, analytical and numerical, corresponding then analyzes behavior that solution limit when slope ramps becomes vertical. second question, obviously linked one, pertains eigenfunction’s its derivative’s continuity at jump points justified as assumption kick-off process, it standardly accepted textbook approaches problem. show that, by following indicated detour, irrelevance eigenfunctions their derivatives turn be proven results instead initial assumptions.