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Exactly Solvable Potentials Derived from SWKB Quantization
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  • Exactly Solvable Potentials Derived from SWKB Quantization
  • Exactly Solvable Potentials Derived from SWKB Quantization
저자명
Sun. Hosung
간행물명
Bulletin of the Korean Chemical Society
권/호정보
2014년|35권 3호|pp.805-810 (6 pages)
발행정보
대한화학회
파일정보
정기간행물|ENG|
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이 논문은 한국과학기술정보연구원과 논문 연계를 통해 무료로 제공되는 원문입니다.
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기타언어초록

The shape invariant potentials are proved to be exactly solvable, i.e. the wave functions and energies of a particle moving under the influence of the shape invariant potentials can be algebraically determined without any approximations. It is well known that the SWKB quantization is exact for all shape invariant potentials though the SWKB quantization itself is approximate. This mystery has not been mathematically resolved yet and may not be solved in a concrete fashion even in the future. Therefore, in the present work, to understand (not prove) the mystery an attempt of deriving exactly solvable potentials directly from the SWKB quantization has been made. And it turns out that all the derived potentials are shape invariant. It implicitly explains why the SWKB quantization is exact for all known shape invariant potentials. Though any new potential has not been found in this study, this brute-force derivation of potentials helps one understand the characteristics of shape invariant potentials.