The Linear Complex PT Symmetric Potential

Abstract A quantum mechanical system with unbroken super-and parity-time (PT)-symmetry is derived and analyzed. Here, we propose a new formalism to construct the complex PT-symmetric superpartners by extending the additive shape invariant potentials to the complex domain. The probabilistic interpretation of a PT-symmetric quantum theory is correlated with the calculation of a new linear operator called the C operator, instead of complex conjugation in conventional quantum mechanics. At the present work, we introduce an anti-PT (A PT) conjugation to redefine a new version of the inner product without any additional considerations. This PT-supersymmetric quantum mechanics, satisfies essential requirements such as completeness, orthonormality as well as probabilistic interpretation.Abstract A quantum mechanical system with unbroken super-and parity-time (PT)-symmetry is derived and analyzed. Here, we propose a new formalism to construct the complex PT-symmetric superpartners by extending the additive shape invariant potentials to the complex domain. The probabilistic interpretation of a PT-symmetric quantum theory is correlated with the calculation of a new linear operator called the C operator, instead of complex conjugation in conventional quantum mechanics. At the present work, we introduce an anti-PT (A PT) conjugation to redefine a new version of the inner product without any additional considerations. This PT-supersymmetric quantum mechanics, satisfies essential requirements such as completeness, orthonormality as well as probabilistic interpretation.

Sep 7, 20210 citations

Three PT-symmetric Hamiltonians with completely different spectra

Francisco Marcelo Fernández, Javier Garcia

We discuss three Hamiltonians, each with a central-field part $H_{0}$ and a PT-symmetric perturbation $igz$ . When $H_{0}$ is the isotropic Harmonic oscillator the spectrum is real for all $g$ because $H$ is isospectral to $H_{0}+g^{2}/2$ . When $H_{0}$ is the Hydrogen atom then infinitely many eigenvalues are complex for all $g$ . If the potential in $H_{0}$ is linear in the radial variable $r$ then the spectrum of $H$ exhibits real eigenvalues for $0We discuss three Hamiltonians, each with a central-field part $H_{0}$ and a PT-symmetric perturbation $igz$. When $H_{0}$ is the isotropic Harmonic oscillator the spectrum is real for all $g$ because $H$ is isospectral to $H_{0}+g^{2}/2$. When $H_{0}$ is the Hydrogen atom then infinitely many eigenvalues are complex for all $g$. If the potential in $H_{0}$ is linear in the radial variable $r$ then the spectrum of $H$ exhibits real eigenvalues for $0

arXiv:1507.03644Jul 13, 20150 citations

A PT-invariant potential with complex QES eigenvalues

Avinash Khare, Bhabani Prasad Mandal

arXiv:quant-ph/0006126Physics Letters AJul 1, 2000165 citations

We discuss three Hamiltonians, each with a central-field part

H_{0}

and a PT-symmetric perturbation

igz

. When

H_{0}

is the isotropic Harmonic oscillator the spectrum is real for all

g

because

H

is isospectral to

H_{0}+g^{2}/2

. When

H_{0}

is the Hydrogen atom then infinitely many eigenvalues are complex for all

g

. If the potential in

H_{0}

is linear in the radial variable

r

then the spectrum of

H

exhibits real eigenvalues for $0