@phdthesis{oai:tsukuba.repo.nii.ac.jp:00008411,
 author = {新堀, 敏基 and Shimbori, Toshiki},
 month = {},
 note = {THE dissertation deals with the two-dimensional isotropic parabolic potential barrier as a solvable model of a two-dimensional unstable system in non-relativistic quantum mechanics. The time-independent Schrodinger equation for this model is set up as the eigenvalue problem in Gel'fand triplet and its exact solutions are expressed by generalized eigen-functions belonging to complex energy eigenvalues. There are stationary states with a real energy eigenvalues. There are statinary states with a real energy eigenvalue involved in those solutions, and they are infinitely degenerate. A physical picture of the generalized eigenstates of the unstable system is obtained from the hydrodynamical point of view. For the first few stationary states of the two-dimensional parabolic potential barrier, the complex velocity potentials in the hydrodynamical formulation of quantum mechanics express the two-dimensional irrotational flows round a right angle. We find that this result can be deduced from the general connection between complex velocity potentials and singular potentials in two-dimensional quantum systems., 2001, Includes bibliographical references},
 school = {筑波大学, University of Tsukuba},
 title = {The hydrodynamical formulation of quantum mechanics and the two-dimensional parabolic potential barrier},
 year = {2002}
}