The widespread availability of spreadsheet software has made it possible to go beyond the graphical approaches which were developed in the days when computing facilities were primitive and scarce. To illustrate the operations involved in such calculations, we use a commercial spreadsheet (Microsoft ® Excel ® ). One of our aims is to reiterate what was pointed out (in the 1970s) after the advent of hand-held electronic calculators : finding the eigenenergies of a finite square well provides a springboard for introducing a physics student to equations whose solutions can only be found through an iterative or recursive technique. We have omitted the last three words of his remark because they should be replaced, in the present context, by the phrase “the last significant digit”. When teaching the finite square well to students, teachers would do well to follow Lord Chesterfield’s advice to his son : “In truth, whatever is worth doing at all is worth doing well, and nothing can be done well without attention: I therefore carry the necessity of attention down to the lowest things, even to …”. Given the elemental nature of the topic, the authors claim no originality with nothing more than the winnowing fork in their hands, they can only clear the threshing floor, gather the wheat into the barn, and let others decide whether or no the chaff should be burnt with unquenchable fire. The purpose of this article is to enable, even encourage, other teachers to give the finite square well the attention that it deserves to this end, the authors provide a tutorial review that is more instructive and comprehensive than the accounts presented in numerous textbooks and dispensed in still more numerous online resources, but does not make any additional demands on the mathematical abilities of the student. The treatment of this topic in standard textbooks has changed little over the last few decades, and such changes as have come to our notice leave, in our opinion, much to be desired. And, of course, with a given relative abundance of elements, a mass density can be computed.A contemporary physicist would be hard put to agree entirely with the author of a 1959 textbook on quantum mechanics, who wrote: “A second simple, one-dimensional system, somewhat divorced from reality but illustrative of the principles of the theory, is a particle in a box with finite walls.” Interest in this prototypic system has not diminished over the years, and is not likely to do so in the near future, because it has now been wedded to reality and is seen as a paradigm for quantum wells and other nanosystems. This will be valuable in obtaining more information about the atmospheres of stars in general, and quasi-stellar objects and X-ray sources in particular, as well as local density variations in the atmosphere of the sun. Astrophysical observations of effective maximum bound states andor maximum distinct levels will enable one to calculate an ion-number density in the source of absorption or emission lines. The effect of screening on the lowering of the ionization potential of an atom is illustrated by the calculation of the observed ionization potential of hydrogen as accurately as it is calculated by more elaborate methods. The concepts and results introduced here also resolve the problem of the intensity drop of hydrogen lines in the solar photosphere and chromosphere and in very low temperature hydrogen in laboratory measurements. The problem of a maximum bound principal quantum number or a finite number of screened Coulomb states has been resolved the screened Coulomb potential yields at least as many bound states as the Coulomb potential. Some numerical solutions of the Schrodinger equation with the complete screened Coulomb potential CSCP have been presented with tables and graphs of quantum numbers lambdasubscripts n, l and relative normalizations phisubscripts n, l lambda.
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