{"title":"关于-对称schavi势的伪范数和可容许解","authors":"G. Lévai","doi":"10.1088/0305-4470/39/32/S17","DOIUrl":null,"url":null,"abstract":"The physically admissible solutions of the -symmetric Scarf I potential are identified in the domain of real and complex energies. It is found that generally there are no admissible complex-energy solutions, and there is one with real energy. In a limited range of the parameters there are two series of seemingly admissible solutions both with the real and complex energies belonging to quasi-parity q = ±; however, the two sets are not -orthogonal in the domain of real energies. The sign of the pseudo-norm of states with real energy is found to oscillate as (−1)n, in accordance with the example of other -symmetric potentials possessing an infinite number of discrete levels. It is argued that the spontaneous breakdown of -symmetry cannot be defined for the Scarf I potential. A comparison with some -symmetric extensions of the infinite square well is presented.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"On the pseudo-norm and admissible solutions of the -symmetric Scarf I potential\",\"authors\":\"G. Lévai\",\"doi\":\"10.1088/0305-4470/39/32/S17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The physically admissible solutions of the -symmetric Scarf I potential are identified in the domain of real and complex energies. It is found that generally there are no admissible complex-energy solutions, and there is one with real energy. In a limited range of the parameters there are two series of seemingly admissible solutions both with the real and complex energies belonging to quasi-parity q = ±; however, the two sets are not -orthogonal in the domain of real energies. The sign of the pseudo-norm of states with real energy is found to oscillate as (−1)n, in accordance with the example of other -symmetric potentials possessing an infinite number of discrete levels. It is argued that the spontaneous breakdown of -symmetry cannot be defined for the Scarf I potential. A comparison with some -symmetric extensions of the infinite square well is presented.\",\"PeriodicalId\":87442,\"journal\":{\"name\":\"Journal of physics A: Mathematical and general\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-08-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of physics A: Mathematical and general\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0305-4470/39/32/S17\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/32/S17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the pseudo-norm and admissible solutions of the -symmetric Scarf I potential
The physically admissible solutions of the -symmetric Scarf I potential are identified in the domain of real and complex energies. It is found that generally there are no admissible complex-energy solutions, and there is one with real energy. In a limited range of the parameters there are two series of seemingly admissible solutions both with the real and complex energies belonging to quasi-parity q = ±; however, the two sets are not -orthogonal in the domain of real energies. The sign of the pseudo-norm of states with real energy is found to oscillate as (−1)n, in accordance with the example of other -symmetric potentials possessing an infinite number of discrete levels. It is argued that the spontaneous breakdown of -symmetry cannot be defined for the Scarf I potential. A comparison with some -symmetric extensions of the infinite square well is presented.