Strong-coupling expansions for the -symmetric oscillators

Fernández, Francisco M.; Guardiola, R.; Ros, J.; Znojil, Miloslav

doi:10.1088/0305-4470/31/50/008

Cited by 134 publications

(102 citation statements)

References 23 publications

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“…Moreover, one can work, alternatively, with the non-standard bra-vectors [25] ψ| → Q · ψ|P ≡ ψ|, Q = ±1 (15) admitting that the norm can be formally indeterminate [26]. This reflects the nonHermiticity of the Hamiltonians and facilitates also the perturbative PT symmetric calculations [31]. The latter coinsiderations leave the consequent interpretation of the PT symmetry still open [32]- [36].…”

Section: Discussionmentioning

confidence: 99%

SPONTANEOUS BREAKDOWN OF $\mathcal{PT}$ SYMMETRY IN THE SOLVABLE SQUARE-WELL MODEL

Znojil

Lévai

2001

Mod. Phys. Lett. A

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Section: Discussionmentioning

confidence: 99%

SPONTANEOUS BREAKDOWN OF $\mathcal{PT}$ SYMMETRY IN THE SOLVABLE SQUARE-WELL MODEL

Znojil

Lévai

2001

Mod. Phys. Lett. A

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“…The first examples of these potentials have even been found using perturbation techniques [19]. Further ones have been identified using semiclassical approximations [5,20] and numerical algorithms [21]. A number of the exactly solvable PT symmetric potentials have been revealed as the analogues of their Hermitian, real special cases [13,15,22,23,24].…”

Section: The Scarf II Potential and Its Pt Symmetric Versionmentioning

confidence: 99%

The interplay of supersymmetry and PT symmetry in quantum mechanics: a case study for the Scarf II potential

Lévai

Znojil

2002

J. Phys. A: Math. Gen.

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Abstract. Motivated by the duality of normalizable states and the presence of the quasi-parity quantum number q = ±1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied. As an illustrative example the PT invariant version of the Scarf II potential is presented, and it is shown that the "bosonic" Hamiltonian has two different "fermionic" SUSY partner Hamiltonians (potentials) generated from the ground-state solutions with q = 1 and q = −1. It is shown that the "fermionic" potentials cease to be PT invariant when the PT symmetry of the "bosonic" potential is spontaneously broken. A modified PT symmetry inspired SUSY construction is also discussed, in which the SUSY charge operators contain the antilinear operator T . It is shown that in this scheme the "fermionic" Hamitonians are just the complex conjugate of the original "fermionic" Hamiltonians, and thus possess the same energy eigenvalues.

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“…For the anharmonic V (x) = x 2 + igx 3 , its perturbative confirmation (viz., the proof using the Borel summability) has even been made available in the early eighties [3]. Very recently, the further numerical and quasi-classical evidence has been provided by the non-polynomial V (x) = x 2 (ix) δ [2] and by its supersymmetric partners [4] as well as by certain hyperbolic [5] and trigonometric [6] models. An additional, purely non-numerical backing of the hypothesis may, last but not least, rely upon the exactly solvable PT symmetric V (x) = exp(ix) [4] and upon the quasiexactly solvable polynomial V (x) = −x 4 + iax 3 + bx 2 + icx [7] and non-polynomial…”

Section: Introductionmentioning

confidence: 99%