Wronskian perturbation theory

P. R. Berman

Paolo Amore, Francisco Marcelo Fernández

We develop a perturbation method that generalizes an approach proposed recently to treat velocity--dependent quantum--mechanical models. In order to test present approach we apply it to some simple trivial and nontrivial examples.

Francisco Marcelo Fernández

We can view equations (8.1) and (8.2) as a system of two linear equations with two unknowns c1 and c2. The determinant of such a system is the Wronskian W(u, v) = uv′ − u′v . (8.3) If W(u, v) is nonzero for some value of x, then the only solution of the system of homogeneous linear equations is c1 = c2 = 0, and the functions are linearly independent. If, on the other hand, W(u, v) is zero for all values of x, then there are solutions for nonzero values of c1 and c2, and the functions are linearly dependent.

D. I. Blokhint︠s︡ev

Jacek Jakiel, W. Kantor

Comparison of non-unitary and generalized unitary scattering theories is done by means of nuclear monodromy (equivalence of Schrödinger and Maxwell time-independent equations), tunneling and radioactivity.Radioactivity is important part of physics and our life.Its importance stretches from medicine as far as to war strategies.We present theoretical approach to achieve better understanding of the radioactive decay when modified quantum theory is applied.It can be done by updating existing codes to understand better construction of the world and terms and conditions of our existence.The theory modifications are strictly connected with the unimodular M matrix and Wronskian matrices (i.e.their determinants named Wronskians) which create underpinning of so called monodromy being two track wave-function evolution.

Alto Osada, Rekishu Yamazaki, Atsushi Noguchi