Large-order perturbation theory for a non-Hermitian 𝓟𝓣-symmetric Hamiltonian

DOI10.1063/1.532991zbMath0969.81019arXivquant-ph/9812039OpenAlexW3105037911MaRDI QIDQ4498442

Publication date: 16 August 2000

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/9812039

zbMATH Keywords

numerical methods energy spectrum ground-state energy Stieltjes function numerical evidence Borel summable complex \({\mathcal P}{\mathcal T}\)-symmetric Hamiltonian high-order Rayleigh-Schrödinger perturbation theory

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Perturbation theories for operators and differential equations in quantum theory (81Q15) Software, source code, etc. for problems pertaining to quantum theory (81-04)

Related Items (40)

Entanglement of multipartite fermionic coherent states for pseudo-Hermitian Hamiltonians ⋮ Solution of effective-mass Dirac equation with scalar-vector and pseudoscalar terms for generalized Hulthén potential ⋮ Many-body excitations in trapped Bose gas: A non-Hermitian approach ⋮ A theoretical method for obtaining Padé type approximation to temperature integrals via the Stieltjes integral ⋮ From generalized Dirac equations to a candidate for dark energy ⋮ Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian ⋮ The effective potential for the PT-symmetric and non-Hermitian \((-g\phi^4)\) field theoretic model ⋮ Mathematical properties of a new Levin-type sequence transformation introduced by Čı́žek, Zamastil, and Skála. I. Algebraic theory ⋮ Higher loop \(\beta\) function for non-Hermitian PT symmetric \(\iota g\phi^3\) theory ⋮ The quasi-exactly solvable potentials method applied to the three-body problem ⋮ Calculation of the characteristic functions of anharmonic oscillators ⋮ Bound-state solutions of the Klein-Gordon equation for the generalized \(PT\)-symmetric hulthén potential ⋮ Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators ⋮ High-order parametrization of the hypergeometric-Meijer approximants ⋮ The analytical transfer matrix method for PT-symmetric complex potential ⋮ Variational perturbation theory for complex cubic potentials ⋮ THE PATH INTEGRAL APPROACH TO AN N-PARTICLE IN A PT-SYMMETRIC HARMONIC OSCILLATOR ⋮ PATH INTEGRALS FOR QUASI-HERMITIAN HAMILTONIANS ⋮ Path integrals for pseudo-Hermitian Hamiltonians ⋮ SUPERSYMMETRIC SOLUTION OF PT-/NON-PT-SYMMETRIC AND NON-HERMITIAN MORSE POTENTIAL VIA HAMILTONIAN HIERARCHY METHOD ⋮ Quantum complex Hénon-Heiles potentials ⋮ Two-point Green's function in PT-symmetric theories ⋮ On an exactly solvable \(B_N\) type Calogero model with non-Hermitian PT invariant interaction ⋮ Multi-instantons and exact results. III: Unification of even and odd anharmonic oscillators ⋮ Multi-instantons and exact results. IV: Path integral formalism ⋮ One-dimensional crystal with a complex periodic potential ⋮ On the eigenproblems of PT-symmetric oscillators ⋮ Extending the range of validity for asymptotic energy expansion method by Padé approximation ⋮ Non-perturbative calculations for the effective potential of the PT symmetric and non-Hermitian (\(-g\varphi ^{4}\)) field theoretical model ⋮ Bound states of non-Hermitian quantum field theories ⋮ Variational treatment for a complex PT-potential ⋮ The Coulomb-harmonic oscillator correspondence in \(\mathcal {PT}\) symmetric quantum mechanics ⋮ A PT-invariant potential with complex QES eigenvalues ⋮ Critical exponents from the weak-coupling, strong-coupling and large-order parametrization of the hypergeometric \((_{k+1}F_k)\) approximants ⋮ PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS ⋮ The stationary optomechanical entanglement between an optical cavity field and a cubic anharmonic oscillator ⋮ Real eigenspectra in non-Hermitian multidimensional Hamiltonians ⋮ EIGENVALUES AND EIGENFUNCTIONS OF WOODS–SAXON POTENTIAL IN PT-SYMMETRIC QUANTUM MECHANICS ⋮ Complex optical potentials and pseudo-Hermitian Hamiltonians ⋮ Aspects of perturbation theory in quantum mechanics: the BenderWu \textsc{Mathematica}\(^{\circledR}\) package

Cites Work

This page was built for publication: Large-order perturbation theory for a non-Hermitian 𝓟𝓣-symmetric Hamiltonian