Asymptotic integration of the second order differential equation, resonance effect
Abstract
There will be presented asymptotic formulas for solutions of the equation
$$
y^'' + ( 1 + \varphi (x) ) y = 0, 0 < x_0 < x < \infty ,
$$
where function $\varphi$ is small in a certain sense for large values of the argument. Usage of method of L-diagonal systems allows to obtain various forms of solutions depending on the properties of function $\varphi$.
The main aim will be discussion about the second order differential equations possesing a resonance effect known for Wigner-von Neumann potential. A class of potentials generalizing that of Wigner-von Neumann will be presented.
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PDFDOI: https://doi.org/10.2478/tatra.v63i0.321