id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-918	Znojil, M.	PT-symmetric Quantum Chain Models	2007	6	.pdf	application/pdf	4992	195	65	It is again unique because one of the two rootsC� � �27 9 21 of the “first alternative” Gröbnerian “effective” equation C C2 54 972� � and both the roots � �354 60 34 of the “sec- ond alternative” equation C C2 708 2916 0� � � are negative, while the only remaining positive root C� � 68 24318125. In the context of the so called Dyson-mapping approximation technique, for exam- ple, it was originally felt as an unpleasant surprise that the requirement of the smallness of the dimension of the matrix H(eff ) emerged in an apparently inseparable combination with the necessity of moving to a less standard Hilbert space H(physical) of states where the definition of the inner (“scalar”) product between elements � � H(physical) and � � H(physical) had to be modified, � � � �� � �� � �, † 0 (1) This trick very easily extends the applicability of the for- malism of standard textbook Quantum Mechanics by the transition to the various nontrivial, “non-Dirac” metric operators.	cache/ap-918.pdf	txt/ap-918.txt