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It is argued that the high energy semiclassical wave functions (SWF) in anarbitrary billiards can be built by approximating the billiards by a respectivepolygon one. The latter billiards is determined by a finite number of periodicorbits of the original one limited by their lengths beginning with the shortestones and which are common for both the billiards. The phenomenon of scars andsuperscars (Heller, E.J., {\it Phys. Rev. Lett.} {\bf 53},(1984) 1515) are thennaturally incorporated into such a construction being a limit of periodic orbitchannels (POCs) considered by Bogomolny and Schmit ({\it Phys. Rev. Lett.} {\bf92} (2004) 244102). The Bunimovich stadium billiards is considered as anexample of such an approach.

High energy semiclassical wave functions in the Bunimovich stadium billiards determined by its periodic orbits