Shannon information entropy sum of the confined hydrogenic atom under the influence of an electric field

Salazar, Saúl J. C.; Laguna, Humberto G.; Dahiya, Brijender; Prasad, Vinod; Sagar, Robin P.

doi:10.1140/epjd/s10053-021-00143-2

Cited by 21 publications

(12 citation statements)

References 91 publications

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“…The edge detection results are evaluated using Shannon Information Entropy (SIE), Precision, Recall, F-Score, and the average time [28]. The SIE believes a system must contain multiple states in order to carry information, and only the more states, the more information it contains [29]. In addition, based on human visual characteristics [30], the SIE is used to evaluate the denoising effect of the proposed method.…”

Section: Measurementioning

confidence: 99%

Edge Detection of COVID-19 CT Image Based on GF_SSR, Improved Multiscale Morphology, and Adaptive Threshold

Hou¹,

Jia²,

Li³

et al. 2022

Computer Modeling in Engineering &Amp; Sciences

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Edge detection is an effective method for image segmentation and feature extraction. Therefore, extracting weak edges with the inhomogeneous gray of Corona Virus Disease 2019 (COVID-19) CT images is extremely important. Multiscale morphology has been widely used in the edge detection of medical images due to its excellent boundary detection accuracy. In this paper, we propose a weak edge detection method based on Gaussian filtering and singlescale Retinex (GF_SSR), and improved multiscale morphology and adaptive threshold binarization (IMSM_ATB). As all the CT images have noise, we propose to remove image noise by Gaussian filtering. The edge of CT images is enhanced using the SSR algorithm. In addition, based on the extracted edge of CT images using improved Multiscale morphology, a particle swarm optimization (PSO) algorithm is introduced to binarize the image by automatically getting the optimal threshold. To evaluate our method, we use images from three datasets, namely COVID-19, Kaggle-COVID-19, and COVID-Chestxray, respectively. The average values of results are worthy of reference, with the Shannon information entropy of 1.8539, the Precision of 0.9992, the Recall of 0.8224, the F-Score of 1.9158, running time of 11.3000. Finally, three types of lesion images in the COVID-19 dataset are selected to evaluate the visual effects of the proposed algorithm. Compared with the other four algorithms, the proposed algorithm effectively detects the weak edge of the lesion and provides help for image segmentation and feature extraction.

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Section: Measurementioning

confidence: 99%

Edge Detection of COVID-19 CT Image Based on GF_SSR, Improved Multiscale Morphology, and Adaptive Threshold

Hou¹,

Jia²,

Li³

et al. 2022

Computer Modeling in Engineering &Amp; Sciences

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“…The Shannon entropy of the confined hydrogenic atoms have been calculated in many previous works 68 – 71 . Very recently, there are studies on the influence of electric field on the Shannon entropy 72 , 73 . As a result, we intend to investigate the analytical and numerical calculation of Shannon entropy and various entropic uncertainty relations 74 – 78 for the Rydberg hydrogen atom, as suggested in the work’s concept.…”

Section: Introductionmentioning

confidence: 99%

Few generalized entropic relations related to Rydberg atoms

Kumar

Prasad

2022

Sci Rep

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We calculate the analytical and numerical values of the position space Shannon entropy, momentum space Shannon entropy, and total Shannon entropy, $$S_\rho$$ S ρ , $$S_\gamma$$ S γ , and $$S_T$$ S T , respectively, of free and trapped Rydberg hydrogen-like atoms. The influence of atomic number Z, the principal quantum number n, and energy E on the Shannon entropy of the Rydberg atoms are illustrated. The scaling properties of Shannon entropy with energy of states E and the principal quantum number n have been reported for the first time to the best of our knowledge. Our work explains how Shannon entropy indicates localization-delocalization of the wavefunction. The total Shannon entropy as a measure of the number of nodes in the trapped Rydberg atom’s wavefunction is also discussed. We show why an uncertainty relation based on Shannon entropy is superior to Heisenberg uncertainty for Rydberg atoms.

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“…Quantum information entropy has been studied widely since Shannon proposed the classical concept in 1948 [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 ]. This is because the Shannon entropy as a measure of uncertainty is a generalization to the traditional Heisenberg relation.…”

Section: Introductionmentioning

confidence: 99%

Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation

Santana-Carrillo

González-Flores

Magaña-Espinal

et al. 2022

Entropy

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In this work we have studied the Shannon information entropy for two hyperbolic single-well potentials in the fractional Schrödinger equation (the fractional derivative number (0<n≤2) by calculating position and momentum entropy. We find that the wave function will move towards the origin as the fractional derivative number n decreases and the position entropy density becomes more severely localized in more fractional system, i.e., for smaller values of n, but the momentum probability density becomes more delocalized. And then we study the Beckner Bialynicki-Birula–Mycieslki (BBM) inequality and notice that the Shannon entropies still satisfy this inequality for different depth u even though this inequality decreases (or increases) gradually as the depth u of the hyperbolic potential U1 (or U2) increases. Finally, we also carry out the Fisher entropy and observe that the Fisher entropy increases as the depth u of the potential wells increases, while the fractional derivative number n decreases.

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Shannon information entropy sum of the confined hydrogenic atom under the influence of an electric field

Cited by 21 publications

References 91 publications

Edge Detection of COVID-19 CT Image Based on GF_SSR, Improved Multiscale Morphology, and Adaptive Threshold

Edge Detection of COVID-19 CT Image Based on GF_SSR, Improved Multiscale Morphology, and Adaptive Threshold

Few generalized entropic relations related to Rydberg atoms

Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation

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