Singular Perturbation of Polynomial Potentials with Applications to Pt -symmetric Families
نویسنده
چکیده
We discuss eigenvalue problems of the form −w+Pw = λw with complex polynomial potential P (z) = tzd+. . ., where t is a parameter, with zero boundary conditions at infinity on two rays in the complex plane. In the first part of the paper we give sufficient conditions for continuity of the spectrum at t = 0. In the second part we apply these results to the study of topology and geometry of the real spectral loci of PT -symmetric families with P of degree 3 and 4, and prove several related results on the location of zeros of their eigenfunctions. MSC: 34M35, 35J10.
منابع مشابه
Singular Perturbation of Polynomial Potentials in the Complex Domain with Applications to Pt -symmetric Families
We discuss eigenvalue problems of the form −w + Pw = λw with complex polynomial potential P (z) = tz + . . ., where t is a parameter, with zero boundary conditions at infinity on two rays in the complex plane. In the first part of the paper we give sufficient conditions for continuity of the spectrum at t = 0. In the second part we apply these results to the study of topology and geometry of th...
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