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We study the problem of a nonrelativistic quantum particle moving on a real line with an idealized and localized singular interaction with zero range at x = 0 (i.e., a point interaction there). This kind of system can be described in two ways: (i) by considering an alternative free system (i.e., without the singular potential) but excluding the point x = 0 (In this case, the point interaction is exclusively encoded in the boundary conditions.) and (ii) by explicitly considering the singular interaction by means of a local singular potential. In this paper we relate, compare, and discuss, in a simple and pedagogical way these two equivalent approaches. Our main goal in this paper is to introduce the essential ideas about point interactions in a very accesible form to advanced undergraduates.

Martensitic AISI 420 stainless steel was plasma nitrided using a DC N2 – H2 pulsed discharge, after thermal treatment at two different tempering temperatures. Sliding wear behavior was determined by means of a ball-on-disk tribometer at room temperature and without lubrication. Wear volume was calculated from the information provided by an optical profilometer and wear scars were analyzed by Scanning Electron Microscopy. The results indicated that the nitrided samples exhibited improved wear resistance when compared to the untreated specimens, but corrosion resistance was diminished due to the presence of the outer nitrided layer. However, when this layer was removed mechanically considerable improvement in the corrosion resistance was achieved without impairing the wear resistance of the whole system, which was 200 % higher compared to the wear resistance of the non-nitrided specimens.

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