We study the behaviour of truncated Rayleigh-Schrödinger series for the low-lying eigenvalues of the one-dimensional, time-independent Schrödinger equation, in the semiclassical limith → 0. Under certain hypotheses on the potential V (x), we prove that for any given smallh > 0 there is an optimal truncation of the series for the approximate eigenvalues, such that the difference between an approximate and exact eigenvalue is smaller than exp(−C/h) for some positive constant C. We also prove the analogous results concerning the eigenfunctions.
A robust technique for achievement 1 GW output power at 1064 nm by amplifying the radiation of diode pumped YAG:NdIYAG:Cr4 microchip-laser in flash lamp pumped amplifier is demonstrated. Compact hybrid laser system with diode pumped microchip master oscillator and two-pass flash lamp pumped amplifier with 300 ps pulse dutation and 300 mJ output energy operating at repetition rate up to 50 Hz is developed. Features of the laser system design are described.
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