schroedinger operator, periodic potential, magnetic field, resonance, asymptotic behaviour of eigenvalue, asymptotic behaviour of eigenfunction.
Essential spectrum of the Schroedinger operator with potentials which are related to the crystal surface was described. The behaviour of bounded solutions of the Schroedinger equation with these potentials was investigated. The asymptotic formula for the eigenvalue (resonance) which appears for small perturbations of periodic potential was obtained. The asymptotic relation between Schroedinger operators with the potentials which correspond crystal film and semi-infinite and infinite crystals was investigated. The existance of the "large number" of non–localized solutions of the Schroedinger equation with limit periodic potential was prooved.
Graduated from Faculty of Mathematics of Voronezh State University in 1973 (department of the patrial differential equations).
Ph.D. thesis was defended in 1979. D.Sci. thesis was defended in 2000. A list of my works contains more than 50 titles.
Chuburin Yu. P. Asimptoticheskoe predstavlenie Floke reshenii uravneniya Shredingera v sluchae poluogranichennogo kristalla // Teor. i matem. fizika, 1988, 77(3), 472–478.
Chuburin Yu. P. O resheniyakh uravneniya Shredingera v sluchae poluogranichennogo kristalla // Teor. i matem. fizika, 1994, 98(1), 38–47.
Chuburin Yu. P. Ob uravnenii Shredingera dlya ploskoi plenki s predelno periodicheskoi reshetkoi // Teor. i matem. fizika, 1996, 106(1), 133–144.
Chuburin Yu. P. O malykh vozmuscheniyakh operatora Shredingera s periodicheskim potentsialom // Teor. i matem. fizika, 1997, 110(3), 443–453.
Chuburin Yu. P. O popadanii sobstvennogo znacheniya (rezonansa) operatora Shredingera na granitsu zony // Teor. i matem. fizika, 2001, 126(2), 196–205.