Abstract
In this work a new scheme is proposed to accurately calculate the rotational energy level of the rigid symmetric-top molecule subjected to the external electric field, and also to obtain the corresponding analytical wave functions. For this purpose, first we use the different forms of function transformation and variable substitution to transform the differential equation of the polar angle θ into a confluent Heun differential equation, and then we use the characteristics of the confluent Heun differential equation and the confluent Heun function to find two linearly dependent solutions of the same eigenstates, which are used to construct the Wronskian determinant to obtain the exact energy spectrum equation. Finally, with the aid of the Maple software, we calculate the eigenvalues for different quantum states, and then substitute the obtained eigenvalues into the unnormalized eigenfunction to obtain the analytical normalized eigenfunction expressed by the confluent Heun function. These results are conducive to the in-depth study of the Stark effect of symmetric-top molecules.
Translated title of the contribution | Exact solutions to Stark effect of rigid symmetric-top molecules |
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Original language | Chinese (Simplified) |
Article number | 180301 |
Journal | Wuli Xuebao/Acta Physica Sinica |
Volume | 70 |
Issue number | 18 |
DOIs | |
State | Published - 20 Sep 2021 |
Keywords
- Confluent Heun function
- Exactly analytic solutions
- Rigid symmetric-top molecules
- Stark effect