TY - JOUR
T1 - Shannon information entropies for position-dependent mass Schrödinger problem with a hyperbolic well
AU - Guo-Hua, Sun
AU - Popov, Dušan
AU - Camacho-Nieto, Oscar
AU - Shi-Hai, Dong
N1 - Publisher Copyright:
© 2015 Chinese Physical Society and IOP Publishing Ltd.
PY - 2015/9/20
Y1 - 2015/9/20
N2 - The Shannon information entropy for the Schrödinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum Sp information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a, while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ(x) for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs(x) and ρs(p) are demonstrated. The Bialynicki-Birula-Mycielski (BBM) inequality is also tested for these states and found to hold.
AB - The Shannon information entropy for the Schrödinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum Sp information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a, while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ(x) for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs(x) and ρs(p) are demonstrated. The Bialynicki-Birula-Mycielski (BBM) inequality is also tested for these states and found to hold.
KW - Fourier transform
KW - Shannon information entropy
KW - hyperbolic potential
KW - position-dependent mass
UR - http://www.scopus.com/inward/record.url?scp=84947461319&partnerID=8YFLogxK
U2 - 10.1088/1674-1056/24/10/100303
DO - 10.1088/1674-1056/24/10/100303
M3 - Artículo
SN - 1674-1056
VL - 24
JO - Chinese Physics B
JF - Chinese Physics B
IS - 10
M1 - 100303
ER -