Self-Similar Interpolation in Quantum Mechanics

An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive interpolation formulae valid in the whole range of parameters of considered physical quantities, the self-similar renormalization procedure is complimented here by boundary conditions which define control functions guaranteeing correct asymptotic behaviour in the vicinity of boundary points. To emphasize the generality of the approach, it is illustrated by different problems that are typical for quantum mechanics, such as anharmonic oscillators, double-well potentials, and quasiresonance models with quasistationary states. In addition, the nonlinear Schr\"odinger equation is considered, for which both eigenvalues and wave functions are constructed.Comment: 1 file, 30 pages, RevTex, no figure

Limited clinical relevance of imaging techniques in the follow-up of patients with advanced chronic lymphocytic leukemia: results of a meta-analysis

The clinical value of imaging is well established for the follow-up of many lymphoid malignancies but not for chronic lymphocytic leukemia (CLL). A meta-analysis was performed with the dataset of 3 German CLL Study Group phase 3 trials (CLL4, CLL5, and CLL8) that included 1372 patients receiving first-line therapy for CLL. Response as well as progression during follow-up was reassessed according to the National Cancer Institute Working Group1996 criteria. A total of 481 events were counted as progressive disease during treatment or follow-up. Of these, 372 progressions (77%) were detected by clinical symptoms or blood counts. Computed tomography (CT) scans or ultrasound were relevant in 44 and 29 cases (9% and 6%), respectively. The decision for relapse treatment was determined by CT scan or ultrasound results in only 2 of 176 patients (1%). CT scan results had an impact on the prognosis of patients in complete remission only after the administration of conventional chemotherapy but not after chemoimmunotherapy. In conclusion, physical examination and blood count remain the methods of choice for staging and clinical follow-up of patients with CLL as recommended by the International Workshop on Chronic Lymphocytic Leukemia 2008 guidelines. These trials are registered at http://www.isrctn.org as ISRCTN 75653261 and ISRCTN 36294212 and at http://www.clinicaltrials.gov as NCT00281918