Fisher information and uncertainty relations for potential family

• Published in: International journal of quantum chemistry Vol. 119; no. 19
• Main Authors: Onate, Clement A., Onyeaju, Michael C., Ikot, Akpan N., Ebomwonyi, Osarodion, Idiodi, John O. A.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 05.10.2019; Wiley Subscription Services, Inc
• Subjects: bound state solutions; Chemistry; expectation value; Fisher information; Physical chemistry; potential term; Quantum physics; Schrodinger equation; Uncertainty; uncertainty relations
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.25991

An approximate bound state solution of the three‐dimensional Schrödinger equation for potential family was obtained together with the corresponding wave function, after which the Fisher information for a potential family was explicitly obtained via the methodology of expectation value and radial expectation value. Some uncertainty relations that are closely related to Heisenberg‐like uncertainty were obtained and numerical results were generated to justify the relations and inequalities. Finally, we have numerically studied the Fisher information for two special cases from the result of the potential family that has applications to prototype systems. It was deduced that the Fisher information of the potential family and that of the two special cases exhibit similar features. The Heisenberg‐like uncertainty relation was obtained for the 3‐D Schrödinger wave equation with related potential family. To justify the relations and inequalities, the position and momentum densities for the two cases studied, revealed the authenticity of the potential family.