Approximate Analytic Expressions for Expectation Values and the “Uncertainty Product” for Even-Power-Series Central Potentials Using the HVT Method

Quantum information entropies for the $$\ell $$ ℓ -state Pöschl–Teller-type potential

“…The expectation value < r −2 > of the Pöschl-Teller-type potential is calculated explicitly, by using the Hellmann-Feynman theorem theorem (HFT) [20,21,[26][27][28][29][30][31][32][33][34]. The HFT states that a non-degenerate eigenvalue E(q) of a parameter-dependent Hermitian operator H(q), the associated eigenvector Ψ(q), changes with respect to the parameter q according to the formula [33,34]:…”

“…This potential is a non-homogeneous potential, as described by Sen and Katriel (2006) [23]. It belongs to a class of even-power series potentials, this class of potentials behave like a harmonic oscillator potential (near the origin), often termed 'oscillator-like' potentials [20,21,25].…”

“…In this study, we shall study the Heisenberg uncertainty principle and the quantum information entropies for the Pöschl-Teller-type potential for any ℓ . As earlier stated, for a particle moving non-relativistically in a central potential V (r), the following uncertainty relation holds ( x = p = 0) [14][15][16][17][18][19][20][21]:…”