Abstract
We generalize Schrödinger’s factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach is the fact that the Hamiltonian is represented as a sum over factorizations in terms of coupled operators that depend on the coordinates and momenta in each Cartesian direction. We determine the eigenstates and energies, the wavefunctions in both coordinate and momentum space, and we also illustrate how this technique can be employed to develop the conventional confluent hypergeometric equation approach. The methodology developed here could potentially be employed for other Hamiltonians that can be represented as the sum over coupled Schrödinger factorizations.
Subject
Condensed Matter Physics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics
Reference34 articles.
1. Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik
2. Quantisierung als Eigenwertproblem
3. Quantisierung als Eigenwertproblem
4. A Method of Determining Quantum-Mechanical Eigenvalues and Eigenfunctions;Schrödinger;Proc. R. Irish Acad. Sec. A Math. Phys. Sci.,1940
5. Further Studies on Solving Eigenvalue Problems by Factorization;Schrödinger;Proc. R. Irish Acad. Sec. A Math. Phys. Sci.,1940
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