Position-momentum uncertainty relations based on moments of arbitrary order

The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by use of the Renyi-entropy-based uncertainty relation. The accuracy of the resulting lower bound is physico-computationally analyzed for the two main prototypes in d-dimensional physics: the hydrogenic and oscillator-like systems.Comment: 31 pages, 9 figure

Entropic integrals of orthogonal hypergeometric polynomials with general supports

The Boltzmann-Shannon information entropy of probability measures which involve the continuous hypergeometric-type polynomials {pn(x)}, orthogonal with respect to a general weight function ω(x), is determined by two integral quantities: one with kernel pn2(x)ω(x) ln pn2(x), called as entropy of the polynomial pn(x), and another one with kernel pn2(x)ω(x) ln ω(x). Here, an explicit expression for the latter quantity, and for a broader family of related integrals, is obtained in terms only of the second-order differential equation satisfied by the involved polynomials. For illustration, the general formula is applied to evaluate the integrals corresponding to the three classical families of continuous orthogonal polynomials on the real axis of hypergeometric type (Hermite, Laguerre, and Jacobi).Publicad