Cartesian operator factorization method for Hydrogen
- URL: http://arxiv.org/abs/2201.01761v1
- Date: Wed, 5 Jan 2022 18:49:37 GMT
- Title: Cartesian operator factorization method for Hydrogen
- Authors: Xinliang Lyu, Christina Daniel, and James K. Freericks
- Abstract summary: We generalize Schroedinger's factorization method for Hydrogen to a Cartesian-based factorization.
We determine the eigenstates and energies, the wavefunctions in both coordinate and momentum space.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We generalize Schroedinger'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 Schroedinger
factorizations.
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