On dynamics of quantum states generated by the Cauchy problem for the Schrödinger equation with degeneration on the half-line
- 18 Downloads
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.
KeywordsCauchy Problem Bounded Operator Regularization Parameter Weak Convergence Cauchy Sequence
Unable to display preview. Download preview PDF.
- 1.S. N. Bakhvalov, V. A. Galkin, and Yu. A. Dubinskii, eds., Works of S. N. Kruzhkov: Collection of Papers [in Russian], Fizmatlit, Moscow (2000), pp. 14–38, 39–45, 99–153, 287–316.Google Scholar
- 3.G. Fichera, “On a unified theory of boundary-value problems for elliptic-parabolic equations of second order,” in: Boundary Problems in Differential Equations, The Univ. of Wisconsin Press, Madison (1960), pp. 97–120.Google Scholar
- 5.A. S. Kholevo, Probabilistic and Statistical Aspects of Quantum Mechanics [in Russian], Nauka, Moscow (1982).Google Scholar
- 6.I. P. Natanson, Function Theory of Real Variables [in Russian], Nauka, Moscow (1974).Google Scholar
- 7.S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems [in Russian], Nauka, Moscow (1969).Google Scholar
- 9.M. Reed and B. Simon, Modern Methods of Mathematical Physics [Russian translation], Vol. 1, Mir, Moscow (1977).Google Scholar