A class of exactly solvable real and complex PT symmetric reflectionless potentials

被引：0

作者：

Banerjee, Suman ^{[1
]}

Yadav, Rajesh Kumar ^{[1
]}

Khare, Avinash ^{[2
]}

Mandal, Bhabani Prasad ^{[3
]}

机构：

[1] Sido Kanhu Murmu Univ, Dept Phys, Dumka 814110, India

[2] Savitribai Phule Pune Univ, Dept Phys, Pune 411007, India

[3] Banaras Hindu Univ, Dept Phys, Varanasi 221005, India

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2024年 / 65卷 / 03期

关键词：

SHAPE-INVARIANT POTENTIALS; NON-HERMITIAN HAMILTONIANS; GROUP THEORETIC APPROACH; SCATTERING-AMPLITUDES; QUANTUM-MECHANICS; EIGENVALUES; EXTENSIONS; FAMILIES;

D O I：

10.1063/5.0174810

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the question of the number of exactly solvable complex but PT-invariant reflectionless potentials with N bound states. By carefully considering the Xm rationally extended reflectionless potentials, we argue that the total number of exactly solvable complex PT-invariant reflectionless potentials are 2[(2N - 1)m + N].

引用

页数：17

共 50 条

[31] Exactly solvable potentials with finitely many discrete eigenvalues of arbitrary choice [J].

Sasaki, Ryu .

JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (06)

[32] Novel quasi-exactly solvable models with anharmonic singular potentials [J].

Agboola, Davids ;

Zhang, Yao-Zhong .

ANNALS OF PHYSICS, 2013, 330 :246-262

[33] SINGULAR PERTURBATION OF POLYNOMIAL POTENTIALS WITH APPLICATIONS TO PT-SYMMETRIC FAMILIES [J].

Eremenko, Alexandre ;

Gabrielov, Andrei .

MOSCOW MATHEMATICAL JOURNAL, 2011, 11 (03) :473-503

[34] Real discrete spectrum in the complex non-PT-symmetric Scarf II potential [J].

Ahmed, Zafar ;

Nathan, Joseph Amal .

PHYSICS LETTERS A, 2015, 379 (10-11) :865-869

[35] PT-symmetric potentials with imaginary asymptotic saturation [J].

Ahmed, Zafar ;

Kumar, Sachin ;

Nathan, Joseph Amal .

PRAMANA-JOURNAL OF PHYSICS, 2022, 96 (03)

[36] Heun functions and quasi-exactly solvable double-well potentials [J].

Chen, Bei-Hua ;

Wu, Yan ;

Xie, Qiong-Tao .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2013, 46 (03)

[37] PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials [J].

Dorey, Patrick ;

Dunning, Clare ;

Lishman, Anna ;

Tateo, Roberto .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (46)

[38] PT-Symmetric Potentials from the Confluent Heun Equation [J].

Levai, Geza .

ENTROPY, 2021, 23 (01) :1-19

[39] New families of non-parity-time-symmetric complex potentials with all-real spectra [J].

Bagchi, Bijan ;

Yang, Jianke .

JOURNAL OF MATHEMATICAL PHYSICS, 2020, 61 (06)

[40] Influence of PT-symmetric complex potentials on the decoupling mechanism in quantum transport processes [J].

Zhang, Lian-Lian ;

Gong, Wei-Jiang ;

Yi, Guang-Yu ;

Du, An .

ANNALS OF PHYSICS, 2020, 416

← 1 2 3 4 5 →