FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 6, PAGES 157-174

On the dynamics of quantum states generated by the Cauchy problem for the Schrödinger equation with degeneration on the half-line

V. Zh. Sakbaev

Abstract

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The paper considers the Cauchy problem for the Schrödinger equation with an operator degenerate on the half-line and the family of regularized Cauchy problems with uniformly elliptic operators whose solutions approximate the solution of the degenerate problem. The author studies the strong and weak convergence of the regularized problems and the convergence of values of quadratic forms of bounded operators on solutions of the regularized problems when the regularization parameter tends to zero.

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Last modified: February 26, 2007