TY - JOUR
T1 - Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation
AU - Santana-Carrillo, R.
AU - González-Flores, Jesus S.
AU - Magaña-Espinal, Emilio
AU - Quezada, Luis F.
AU - Sun, Guo Hua
AU - Dong, Shi Hai
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/11
Y1 - 2022/11
N2 - 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 (Formula presented.) 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 (Formula presented.) (or (Formula presented.)) 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.
AB - 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 (Formula presented.) 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 (Formula presented.) (or (Formula presented.)) 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.
KW - Fisher entropy
KW - Shannon entropy
KW - fractional Schrödinger equation
KW - hyperbolic potential well
UR - http://www.scopus.com/inward/record.url?scp=85141666376&partnerID=8YFLogxK
U2 - 10.3390/e24111516
DO - 10.3390/e24111516
M3 - Artículo
C2 - 36359609
AN - SCOPUS:85141666376
SN - 1099-4300
VL - 24
JO - Entropy
JF - Entropy
IS - 11
M1 - 1516
ER -