In this work, we present the exact solution of the bosonic oscillator subjected to the interaction of an uniform electric field on the de Sitter and anti de Sitter spaces. In both cases, we extract the energy spectrum and the associated wave functions. For de Sitter case, the wave functions are expressed according to the Jacobi polynomial and for anti de Sitter case, the wave functions are expressed according to Romanovski’s polynomial. Finally the limiting cases are studied.

中文翻译：

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德西特空间和反德西特空间上的玻色子振荡器

在这项工作中，我们提出了在德西特和反德西特空间上受到均匀电场相互作用的玻色振子的精确解。在这两种情况下，我们都提取了能谱和相关的波函数。对于德西特情况，波函数根据雅可比多项式表示，对于反德西特情况，波函数根据罗曼诺夫斯基多​​项式表示。最后研究了极限情况。