Summary
Vibrational-rotational coupling in diatomic molecules has been studied by three different approaches through the solution of Schrödinger equation with a new potential. In the first and second approaches called, respectively, the closed-form method and the factorization method, analytical expressions for the energy levels, wave functions and various spectroscopic constantsviz.,α e and ωe x e have been derived. In the third method, the said potential has been treated as the Morse one with some perturbations added to it, and the perturbation method has been employed to determine the energy levels and wave functions as corrections to those for the Morse potential. In this calculation a harmonicoscillator wave function has been used as the unperturbed wave function.
Riassunto
Si è studiato l’accoppiamento vibrazionale-rotazionale nelle molecole diatomiche per tre diversi approcci attraverso la soluzione dell’equazione di Schrödinger per un nuovo potenziale. Nel primo e nel secondo approccio, chiamati rispettivamente metodo di forma chiusa e metodo di fattorizzazione, si sono derivate espressioni analitiche per i livelli di energia, funzioni d’onda e varie costanti spettroscopiche, cioè αe e ωe x e. Nel terzo metodo il suddetto potenziale è stato trattato come quello di Morse con l’aggiunta di alcume perturbazioni, e il metodo delle perturbazioni è stato impiegato per determinare i livelli di energia e le funzioni d’onda come correzioni per il potenziale di Morse. In questo calcolo si è usata la funzione d’onda per l’oscillatore armonico come funzione d’onda non perturbata.
Резюме
Исследуется вибрационно-ротационная связь в двухатомных молекулах, используя три подхода при решении уравнения Шредингера с новым потенциалом. В первом и во втором подходах, называемых соответственно метод замкнутой формы и метод факторизации, выводятся аналитические выражения для уровней энергии, волновых функций и различных спектроскопических постоянных αe и ωe x e. В третьем подходе рассматриваемый потенциал трактуется как потенциал Морса с некоторыми возмущениями. Затем используется теория возмущений для определения энергетических уровней и волновых функций, причем, в качестве невозмущенных величин используются результаты, полученные с потенциалом Морса. В этих вычислениях в качестве невозмущенной волновой функции испольеуется волновая функция гармонического осциллятора.
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References
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Mohammad, S.N. Calculations of vibrational-rotational coupling constants in diatomic molecules. Nuov Cim B 49, 124–134 (1979). https://doi.org/10.1007/BF02737480
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DOI: https://doi.org/10.1007/BF02737480