Fisher information entropies and the strength of an oscillator under a mixed hyperbolic Pöschl–Teller potential function

• Published in: Indian journal of physics Vol. 97; no. 12; pp. 3411 - 3417
• Main Authors: Omugbe, E., Osafile, O. E., Okon, I. B., Jahanshir, A., Njoku, I. J., Onate, C. A.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01-10-2023; Springer Nature B.V
• Subjects: Astrophysics and Astroparticles; Eigenvalues; Energy spectra; Fisher information; Hyperbolic functions; Information theory; Original Paper; Oscillators; Parameters; Physics; Physics and Astronomy; Potential energy; Wave functions; Super-symmetric WKB method; Pöschl–Teller potential; Fisher information entropies; Oscillator strengths; Cramer–Rao inequalities
• ISSN: 0973-1458; 0974-9845
• DOI: 10.1007/s12648-023-02676-1

The Fisher information-theoretic measurement and the oscillator strength are studied with a mixed hyperbolic Pöschl–Teller potential (MHPTP). Using the total energy eigenvalue equation obtained via the super-symmetric WKB approach as well as the total wave function. We obtained the oscillator strength for the atomic transitions
1
s
-
2
p
and
1
s
-
3
p
, where the strength length decreased with increasing potential screening parameters. Also, the Fisher information entropies for both position and momentum spaces are obtained numerically. We studied the correlation between potential parameters and the energy spectra graphically. Our results for the information-theoretic measures obey the Fisher's uncertainty product and the Cramer–Rao inequality in position space. The analytical result for the
N
-dimensional energy eigenvalue obtained by the super-symmetric WKB approach is the same as the result obtained by a different analytic approach in the existing literature. The oscillator strength conforms to the ones reported in existing literature using different potential energy functions.