We show the coherence properties of a signal can be measured by a Hartmann wavefront sensor in a nonclassical regime. Recasting the detection theory of the classical Hartmann sensor in the sense of quantum tomography enables to measure the coherence function, which is an analogy to the density matrix of mixed quantum states. Two methods were tested for the reconstruction of the coherence matrix from the intensity scan in the nonclassical mode of the Hartmann sensor. The reconstruction was performed in a classic way using the POVM matrix and using data pattern tomography.We show the coherence properties of a signal can be measured by a Hartmann wavefront sensor in a nonclassical regime. Recasting the detection theory of the classical Hartmann sensor in the sense of quantum tomography enables to measure the coherence function, which is an analogy to the density matrix of mixed quantum states. Two methods were tested for the reconstruction of the coherence matrix from the intensity scan in the nonclassical mode of the Hartmann sensor. The reconstruction was performed in a classic way using the POVM matrix and using data pattern tomography.

EPJ Web of ConferencesJan 1, 20220 citations

Coherent states for general potentials

A. D. Jannussis, V. Papatheou, N. Patargias +1 more

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJul 1, 19818 citations

BOUND STATES OF KLEIN-GORDON EQUATION FOR HARTMANN SCALAR AND VECTOR POTENTIALS

Fa‐Lin Lu

By using the usual method of variable separation, bound states of Klein-Gordon equation with equal Hartmann scalar and vector potentials are solved. Properties of the system relate to three quantum numbers and parameters of Hartmann potential. The normalized angle wave function expressed in terms of the universal associated-Legendre polynomial and the normalized radial wave function expressed in terms of the confluent hypergeometric function are presented. The exacl energy spectrum equations are obtained. Bound states of Klein-Gordon equation for Hydrogen potential are special cases for the Hartmann potential in the Letter.By using the usual method of variable separation, bound states of Klein-Gordon equation with equal Hartmann scalar and vector potentials are solved. Properties of the system relate to three quantum numbers and parameters of Hartmann potential. The normalized angle wave function expressed in terms of the universal associated-Legendre polynomial and the normalized radial wave function expressed in terms of the confluent hypergeometric function are presented. The exacl energy spectrum equations are obtained. Bound states of Klein-Gordon equation for Hydrogen potential are special cases for the Hartmann potential in the Letter.

Journal of Anhui Normal UniversityJan 1, 20050 citations

Supersymmetry and the Hartmann Potential of Theoretical Chemistry

Gardo Blado

The ring-shaped Hartmann potential $ V = ησ^{2} ε_{0} \left( \frac{2 a_{0}}{r} - \frac{ηa_{0}^{2}}{r^{2} sin^{2} θ} \right) $ was introduced in quantum chemistry to describe ring-shaped molecules like benzene. In this article, the supersymmetric features of the Hartmann potential are discussed. We first review the results of a previous paper in which we rederived the eigenvalues and radial eigenfunctions of the Hartmann potential using a formulation of one-dimensional supersymmetric quantum mechanics (SUSYQM) on the half-line $\left[ 0, \infty \right)$ . A reformulation of SUSYQM in the full line $\left( -\infty, \infty \right)$ is subsequently developed. It is found that the second formulation makes a connection between states having the same quantum number $L$ but different values of $ησ^{2}$ and quantum number $N$ . This is in contrast to the first formulation, which relates states with identical values of the quantum number $N$ and $ησ^{2}$ but different values of the quantum number $L$ .The ring-shaped Hartmann potential $ V = ησ^{2} ε_{0} \left( \frac{2 a_{0}}{r} - \frac{ηa_{0}^{2}}{r^{2} sin^{2} θ} \right) $ was introduced in quantum chemistry to describe ring-shaped molecules like benzene. In this article, the supersymmetric features of the Hartmann potential are discussed. We first review the results of a previous paper in which we rederived the eigenvalues and radial eigenfunctions of the Hartmann potential using a formulation of one-dimensional supersymmetric quantum mechanics (SUSYQM) on the half-line $\left[ 0, \infty \right)$. A reformulation of SUSYQM in the full line $\left( -\infty, \infty \right)$ is subsequently developed. It is found that the second formulation makes a connection between states having the same quantum number $L$ but different values of $ησ^{2}$ and quantum number $N$. This is in contrast to the first formulation, which relates states with identical values of the quantum number $N$ and $ησ^{2}$ but different values of the quantum number $L$.

arXiv:quant-ph/9602005Feb 8, 19960 citations

\left[ 0, \infty \right)

. A reformulation of SUSYQM in the full line

\left( -\infty, \infty \right)

is subsequently developed. It is found that the second formulation makes a connection between states having the same quantum number

L

but different values of

ησ^{2}

and quantum number

N

. This is in contrast to the first formulation, which relates states with identical values of the quantum number

N

and

ησ^{2}

but different values of the quantum number

L