A Schrödinger equation for a well potential with varying width is studied. Generalized canonical transformations are shown to transform the problem into a time-dependent harmonic oscillator problem submitted to fixed boundary conditions. This transformed problem is solved by a perturbation technique and gives the evolution of the average energy of the system according to the motion of the well. Motions corresponding to a renormalization or compaction group are shown to be solvable by separation of variables.

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Background/aim-Blindness in the developed countries aVects 3.5 million people. This study was conducted on the causes of blindness in the Republic of Ireland based on the register of the National Council for the Blind of Ireland. The aim was to determine the prevalence of potentially avoidable blindness and to identify its causes. Method-Criteria for registration as blind are in Ireland: best corrected visual acuity of 6/60 (0.1) or less in the better eye or a visual field restricted to 20 degrees or less. Data on 5002 adults 16 years an older registered as blind were analysed. The causes of blindness are classified in 17 diagnostic categories. Results-The leading causes of blindness are macular degeneration and glaucoma, each accounting for 16% (812 and 795). Cataract accounted for 11% (561), a third of these had an associated cause of blindness and one tenth had a cognitive deficit. Diabetic retinopathy ranked as the 11th cause of blindness and accounted for 3% (147). More than half of the patients were 65 years and older. Conclusion-25% of blindness was potentially avoidable. The treatable causes were glaucoma and diabetic retinopathy in the working population and glaucoma and cataract over 65 years of age. Glaucoma is the most important, which raises the question of a screening programme. The prevalence of blindness of 3% due to diabetic retinopathy is lower than in most other series. (Br J Ophthalmol 1998;82:630-633)

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Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.