TY - JOUR
AU - Rajchel, Kazimierz
PY - 2019/09/25
Y2 - 2024/10/16
TI - Solutions of the time-independent SchrÃ¶dinger equation by uniformization on the unit circle
JF - Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica
JA - Ann. Univ. Paedagog. Crac. Stud. Math.
VL - 18
IS -
SE - Published
DO -
UR - https://studmath.uken.krakow.pl/article/view/7951
SP - 157-165
AB - <p>The idea presented here of a general quantization rule for bound states is mainly based on the Riccati equation which is a result of the transformed, time-independent, one-dimensional SchrÃ¶dinger equation. The condition imposed on the logarithmic derivative of the ground state function W0 allows to present the Riccati equation as the unit circle equation with winding number equal to one which, by appropriately chosen transformations, can be converted into the unit circle equation with multiple winding number. As a consequence, a completely new quantization condition, which gives exact results for any quantum number, is obtained.</p>
ER -