کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5495804 1529828 2017 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Dirichlet spectra of the paradigm model of complex PT-symmetric potential: V(x)=−(ix)N
موضوعات مرتبط
مهندسی و علوم پایه فیزیک و نجوم فیزیک و نجوم (عمومی)
پیش نمایش صفحه اول مقاله
Dirichlet spectra of the paradigm model of complex PT-symmetric potential: V(x)=−(ix)N
چکیده انگلیسی
So far the spectra En(N) of the paradigm model of complex PT(Parity-Time)-symmetric potential VBB(x,N)=−(ix)N is known to be analytically continued for N>4. Consequently, the well known eigenvalues of the Hermitian cases (N=6,10) cannot be recovered. Here, we illustrate Kato's theorem that even if a Hamiltonian H(λ) is an analytic function of a real parameter λ, its eigenvalues En(λ) may not be analytic at finite number of Isolated Points (IPs). In this light, we present the Dirichlet spectra En(N) of VBB(x,N) for 2≤N<12 using the numerical integration of Schrödinger equation with ψ(x=±∞)=0 and the diagonalization of H=p2∕2μ+VBB(x,N) in the harmonic oscillator basis. We show that these real discrete spectra are consistent with the most simple two-turning point CWKB (C refers to complex turning points) method provided we choose the maximal turning points (MxTP) [−a+ib,a+ib,a,b∈R] such that |a| is the largest for a given energy among all (multiple) turning points. We find that En(N) are continuous function of N but non-analytic (their first derivative is discontinuous) at IPs N=4,8; where the Dirichlet spectrum is null (as VBB becomes a Hermitian flat-top potential barrier). At N=6 and 10, VBB(x,N) becomes a Hermitian well and we recover its well known eigenvalues.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Physics - Volume 383, August 2017, Pages 635-644
نویسندگان
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