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Exact solutions of the rigid rotor in the electric field
Author(s) -
Chen ChangYuan,
Wang XiaoHua,
You Yuan,
Sun GuoHua,
Dong ShiHai
Publication year - 2020
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.26336
Subject(s) - wronskian , eigenvalues and eigenvectors , degeneracy (biology) , rigid rotor , electric field , perturbation (astronomy) , rotor (electric) , angular momentum , physics , perturbation theory (quantum mechanics) , mathematical physics , mathematics , quantum mechanics , bioinformatics , biology
We first present a new constraint condition on the confluent Heun function H C ( α , β , γ , δ , η ; z ) ( β , γ ≥ 0, z ∈ [0, 1]) and then illustrate how to solve the rigid rotor in the electric field. We find its exact solutions unsolved previously through solving the Wronskian determinant. The present results compared with those by the perturbation methods are found to have a big difference for a large parameter a . We also present 2D and 3D probability density distributions by choosing different angular momentum quantum numbers l . We observe that the original eigenvalues with degeneracy (2 l + 1) are split into the ( l + 1) state with approximate eigenvalues l ( l + 1) for small a but large l .