Journal of Mathematical Sciences

, Volume 151, Issue 1, pp 2741–2753 | Cite as

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.


Cauchy Problem Bounded Operator Regularization Parameter Weak Convergence Cauchy Sequence 
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© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyRussia

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