The Runge-Lenz vector possesses specific eigenfunctions in quantum mechanics.
The claim is supported by quantum mechanical studies showing that components of the Runge-Lenz vector interact directly with hydrogen atom eigenfunctions and wavefunctions.
The retrieved literature clearly discusses the quantum mechanical operator form of the Runge-Lenz (Laplace-Runge-Lenz) vector and its operation on or relation to hydrogenic eigenfunctions (such as spherical harmonics and hybrid orbitals) in quantum mechanics. Papers [5] and [11] specifically detail how these operators function on eigenfunctions, confirming the claim.
C. E. Burkhardt, J. J. Leventhal. Lenz vector operations on spherical hydrogen atom eigenfunctions. 2004. https://doi.org/10.1119/1.1758225
Paper [5] demonstrates how components of the quantum mechanical Lenz vector operator convert certain spherical hydrogen atom eigenfunctions into others by raising the angular momentum quantum number.
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Lawrence L. Lohr. Hybrid orbitals and the runge–lenz vector. 1976. https://doi.org/10.1002/qua.560100511
Paper [11] explicitly examines matrix elements and properties of the Runge-Lenz vector with respect to specific hydrogenic wavefunctions and hybrid orbitals.
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