Generalized Cramér-Rao relations for non-relativistic quantum systems

Jesus S Dehesa (1) , Angelo R. Plastino (2) , Pablo Sanchez-Moreno (3, 4) , Christophe Vignat (5)

1 Instituto de Física Teórica y Computacional Carlos I and Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada
2 Depto. de Fisica,
3 Instituto Carlos I de Fisica Teorica y Computacional
4 Departamento de Matemática Aplicada
5 L2S - Laboratoire des signaux et systèmes

The Cramer-Rao product of the Fisher information F[rho] and the variance < x(2)> equivalent to integral x(2) rho(x)dx of a probability density rho(x), defined on a domain Omega subset of R-D, is found to have a minimum value reached by the density associated with the ground state of the harmonic oscillator in Omega, when Omega is an unbounded domain. If Omega is bounded, the minimum value of the Fisher information is achieved by the ground state of the quantum box described itself by this domain. (

Domaines: Sciences de l'ingénieur [physics]

Jesus S Dehesa, Angelo R. Plastino, Pablo Sanchez-Moreno, Christophe Vignat. Generalized Cramér-Rao relations for non-relativistic quantum systems. Applied Mathematics Letters, 2012, 25 (11), pp.1689-1694. ⟨10.1016/j.aml.2012.01.038⟩. ⟨hal-00831856⟩