Wave functions of the Hydrogen atom in the momentum representation

We construct the integral transform passing from the space representation to the momentum representation for the Hydrogen atom using polar spherical coordinates. The resulting radial wave functions are explicitly given in terms of complex finite expansions of Gegenbauer functions of the first and second kind, or in terms of (elementary) trigonometric functions. We show their symmetry under the $SO(4)$ group, and their equivalence with those of Lombardi and Oglivie.Comment: Revised version, according to the referees' suggestions. Includes new figure

Classifying fibromyalgia patients according to severity: the combined index of severity in fibromyalgia

The aim of this study was to establish the cutoff points in the Combined Index of Fibromyalgia Severity (ICAF) questionnaire which allow classification of patients by severity and to evaluate its application in the clinical practice. The cutoff points were calculated using the area under the ROC curve in two cohorts of patients. Three visits, basal, fourth month and 15th month, were considered. The external criterion for grading severity was the number of drugs consumed by the patient. Sequential changes were calculated and compared. Correlations with drug consumption and comparisons of severity between patients with different types of coping were also calculated. Correlation between the number of drugs and the ICAF total score was significant. Three cutoff points were established: absence of Fibromyalgia (FM), <34; mild, 34–41; moderate, 41–50 and severe, >50, with the following distribution of severity: absence in 0.4 %, mild in 18.7 %, moderate in 32.5 % and severe in 48.4 % of the patients. There were significant differences between groups. The treatment under daily clinical conditions showed a significant improvement of the patients which was maintained at the end of follow-up. There was a 17 % reduction in the severe category. The patients with more passive coping factor showed highest punctuations in the remaining scores and were more prevalent in the severe category. The patients with a predominance of the emotional factor showed a better response at the end of follow-up. The established cutoff points allow the classification of FM patients by severity, to know the prognostic and to predict the response to the treatment

Exactitud del método de monitorización de la frecuencia cardíaca en la estimación del coste energético

El método de monitorización de la frecuencia cardíaca (MFC) es utilizado para la estimación de la energía gastada. Sin embargo, una de las principales críticas a dicho método es su exactitud. Por ello que nuestro estudio se centró en cuantificar la exactitud del referido método cuando se aplica a diferentes intensidades de esfuerzo. Participaron 9 sujetos que realizaron primero una ergoespirometría para la determinación de la recta VO2-FC y otra posterior para comparar la estimación con los resultados del VO2 medido. No existen diferencias entre el VO2 estimado y medido. El porcentaje de error medio fue de 1.47%, ocurriendo el mayor porcentaje de error a la intensidad más baja. Diferenciando por sexos, ocurre que para las mujeres el VO2 se sobrestima y en los hombres se subestima. Este método es de una elevada relación beneficio/coste por lo que puede ser de gran utilidad en estudios de poblaciones