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Cartesian Operator Factorization Method for Hydrogen
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.
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- NSF-PAR ID:
- 10343033
- Date Published:
- Journal Name:
- Atoms
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2218-2004
- Page Range / eLocation ID:
- 14
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/atoms10010014
