Information-theoretic measures for a solitonic profile mass Schrödinger equation with a squared hyperbolic cosecant potential

• Solutions to solitonic profile mass Schrödinger equation with squared hyperbolic cosecant potentials are obtained.
• Such a study might be interesting to those experimental physicists in condensed matter physics.
• The position entropy is calculated considering the singular point.
• The complicated Fourier transforms are derived.
• BBM inequality is verified.

Entropic measures provide analytic tools to help us understand the stability of quantum systems. The spreading of the quantum-mechanical probability cloud for solitonic profile mass Schrödinger equation with a potential V(ax)=−V0csch2(ax) is studied in position and momentum space by means of global (Shannon’s information entropy) information-theoretic measures. The position information entropy is considered only for x>0x>0 due to the singular point at x=0x=0. The entropy densities ρs(x)ρs(x) and ρs(p)ρs(p) are demonstrated and the BBM inequality is saturated.