Erratum to: Eigenvalues of a harmonic oscillator in the ultrarelativistic limit

Abstract

Subjec t of th i s no te is t h e s -wave SchrSdinger equa t ion w i t h re la t iv i s t i c kinema t i c s (1.7) in t he case of h a r m o n i c osci l la tor of zero mass (u l t ra re la t iv i s t i c l imi t ) . W e shal l com pa re the resu l t s of a W K B approach to t h a t equa t ion (s) w i t h t he exac t ones wh ich are ob ta inab le by the ana ly t i ca l solut ion in t h e impulse space. This suppl ies an useful t e s t for our W K B me thod , especial ly as for t he usual SchrSdinger equa t ion w i t h t h e h a r m o n i c po t en t i a l t he s t a n d a r d W K B m e t h o d yields t h e exac t spec t rum. As we shal l see, some th ing l ike t h a t ho lds for our equa t ion . As for t h e harmonic -osc i l l a to r po ten t i a l , we m e n t i o n t h a t i t was i n t r o d u c e d as a q u a r k a n t i q u a r k po t en t i a l in a re la t iv i s t ic mode l by F~YNMAN et al. (9) for t h e calculat ion of cur rents . I t was app l ied b y RAVNDAL (10,11) to ep sca t t e r ing and to t h e weak p r o d u c t i o n of resonances , by COPLEY et al. (12) to t h e e l ec t rop roduc t ion of nucleonic