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

The paper considers the Cauchy problem for the Schrödinger equation with operator degenerate on the semiaxis 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 convergences 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. © 2008 Springer Science+Business Media, Inc.