Computing Dirichlet eigenvalues of the Schrödinger operator with a PT-symmetric optical potential

NUR, Cemile

doi:10.1186/s13661-023-01787-2

Computing Dirichlet eigenvalues of the Schrödinger operator with a PT-symmetric optical potential

Yazarlar (1)

Doç. Dr. Cemile NUR Yalova Üniversitesi, Türkiye

Makale Türü	Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
Dergi Adı	Boundary Value Problems, Springer Science and Business Media LLC (Q1)
Dergi ISSN	1687-2770 Wos Dergi Scopus Dergi
Dergi Tarandığı Indeksler	SCI-Expanded
Makale Dili	Türkçe	Basım Tarihi	10-2023
Kabul Tarihi	28-09-2023	Yayınlanma Tarihi	04-10-2023
Cilt / Sayı / Sayfa	2023 / 98 / –	DOI	10.1186/s13661-023-01787-2
Makale Linki	http://dx.doi.org/10.1186/s13661-023-01787-2

Özet

AbstractWe provide estimates for the eigenvalues of non-self-adjoint Sturm–Liouville operators with Dirichlet boundary conditions for a shift of the special potential

$4\cos ^{2}x+4iV\sin 2x$

4

cos
2

x
+
4
i
V
sin
2
x
that is a PT-symmetric optical potential, especially when

$|c|=|\sqrt{1-4V^{2}}|<2$

|
c
|
=
|

1
−
4

V
2

|
<
2
or correspondingly

$0\leq V<\sqrt {5}/2$

0
≤
V
<

5

/
2
. We obtain some useful equations for calculating Dirichlet eigenvalues also for

$|c|\geq 2$

|
c
|
≥
2
or equally

$V\geq \sqrt{5}/2$

V
≥

5

/
2
. We discuss our results by comparing them with the periodic and antiperiodic eigenvalues of the Schrödinger operator. We even approximate complex eigenvalues by the roots of some polynomials derived from some iteration formulas. Moreover, we give a numerical example with error analysis.

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Atıf Sayıları

Computing Dirichlet eigenvalues of the Schrödinger operator with a PT-symmetric optical potential

Dergi Adı	Boundary Value Problems
Yayıncı	SpringerOpen
Açık Erişim	Evet
ISSN	1687-2770
E-ISSN	1687-2770
CiteScore	2,0
SJR	0,479
SNIP	0,825

Computing Dirichlet eigenvalues of the Schrödinger operator with a PT-symmetric optical potential

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