T h e pu rpose of th i s n o t e is to g ive a gene ra l i za t ion of t he L e v y a n d Kel ler (1} m e t h o d for f ind ing t h e phase shif ts . L e t r l y ( r ) d e n o t e t he r ad i a l wave func t ion , for a pa r t i c l e in t he p resence of spher i ca l ly s y m m e t r i c p o t e n t i a l (h-° /2y)[V( ' r ) (a / r ) ] , t h e n t h e SchrSd inger e q u a t i o n is g iven b y (1) y" Jr [k 2 + ( a / r ) V ( r ) l ( | + 1)/r2]y = 0 . T h e so lu t ion y(r) shou ld be regu la r a t t he origin, a n d the re fore we h a v e (2) y(O)= 0. In eq. (1) t h e wave n u m b e r k, as known, is r e l a t ed to t he e n e r g y E of t he part iele b y t h e r e l a t i on k 2 = 2 f f E / h 2, 1 is an a n g u l a r m o m e n t u m q u a n t u m n u m b e r a n d a is ~ c o n s t a n t . W e assume t h a t V(r) b e h a v e s a t r = 0 no more s ingular t h a n (1/r ~) a n d for large "r vMues goes to zero f a s t e r t h a n (l/r2). In o rde r to o b t a i n an e q u a t i o n for t i le p h a s e shi f t s 6, we i n t r o d u c e two l inear i n d e p e n d e n t so lu t ion u(r) a n d v(r) of eq. ( l ) for V ( r ) ~ 0. F o r large r va lues we chose for u(r) and r(r) t h e fol lowing a sympto t i c fo rms :