Factorization of the radial Schrödinger equation and four kinds of raising and lowering operators of hydrogen atoms and isotropic harmonic oscillators

• Published in: Physics letters. A Vol. 231; no. 1; pp. 9 - 22
• Main Authors: Liu, Y.F., Lei, Y.A., Zeng, J.Y.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 30-06-1997
• Subjects: 03.65.Ge; 03.65.−w
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/S0375-9601(97)00256-9

It was shown that only for the Coulomb potential and isotropic harmonic oscillator the radial Schrödinger equation can be factorized. Directly from the factorization, two kinds of raising and lowering operators for the isotropic harmonic oscillator, but only one for the hydrogen atom, can be derived. Four kinds of raising and lowering operators connecting the nearest neighboring eigenstates were investigated.