Quantum section method for the soft stadium (Q1589747)

One should probably start reading this paper from its very end. Indeed, appendix B explains the essence of the section method on an elementary solvable example (which is just generalized to a ``soft stadium'' in the bulk text). Appendix A then offers more details on the usual exact solution for comparison, and the reader is prepared to study the preceding text devoted to the unsolvable intermediate cases (hint and motivation: the standard billiard for study of the quantum chaos is obtained in the large-exponent limiting case). In the spirit of the method, a dissection of the general system is to be performed in such a way that the subsystems remain separable (and the method applicable) and, by our recommendation, one first looks at section 8 where the results of the comparison of the Appendices are presented in three comprehensible figures. Then we are prepared to accept the main message (section 9) and get easily convinced that the transition to chaos is controlled by the level repulsion and that a good agreement with the hard-billiard data is achieved comparatively soon (for the variable ``measure of softness'' equal to cca 13). At this point, one already has enough time and returns to the technicalities (especially, to the reliable evaluation of overlaps using WKB approximants in the short secs. 4 through 6) and, in the last step, indulges in reading about the method itself (sec. 3) and about its historical and classical background (secs. 1 and 2).