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Algebraic approach to radial ladder operators in the hydrogen atom
Author(s) -
MartínezYRomero R. P.,
NúñezYépez H. N.,
SalasBrito A. L.
Publication year - 2007
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21317
Subject(s) - casimir element , ladder operator , eigenfunction , hamiltonian (control theory) , hydrogen atom , algebra over a field , operator (biology) , mathematics , algebraic number , current algebra , mathematical physics , physics , pure mathematics , eigenvalues and eigenvectors , quantum mechanics , compact operator , chemistry , affine lie algebra , extension (predicate logic) , mathematical analysis , computer science , repressor , mathematical optimization , biochemistry , transcription factor , programming language , group (periodic table) , gene
We add a phase variable and its corresponding operator to the description of the hydrogen atom. With the help of these additions, we device operators that act as ladder operators for the radial system. The algebra defined by the commutation relations between those operators has a Casimir operator coincident with the radial Hamiltonian of the problem. The algebra happens to be the well‐known su (1,1) Lie algebra, hence the phase‐dependent eigenfunctions calculated within our scheme belong in a representation of that algebra, a fact that may be useful in certain applications. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007