Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians


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Bender C., Berry M., Meisinger P., Savage V., Simsek M.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, cilt.34, sa.6, 2001 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Kısa Makale
  • Cilt numarası: 34 Konu: 6
  • Basım Tarihi: 2001
  • Doi Numarası: 10.1088/0305-4470/34/6/101
  • Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL

Özet

The Hamiltonian H = p(2)+x(4)+iAx, where A is a real parameter, is investigated. The spectrum of H is discrete and entirely real and positive for \A\ < 3.169. As \A\ increases past this point, adjacent pairs of energy levels coalesce and then become complex, starting with the lowest-lying energy levels. For large energies, the values of A at which this merging occurs scale as the three-quarters power of the energy. That is, as \A\ --> infinity and E --> infinity, at the points of coalescence the ratio a = \A\E-3/4 approaches a constant whose numerical value is a(crit) = 1.1838363072914. Conventional WKB theory determines the high-lying energy levels but cannot be used to calculate a(crit). This critical value is predicted exactly by complex WKB theory.