In the context of new type of the extended uncertainty principle using the displacement operator method, we present an exact solution of some problems such as: the Klein–Gordon particle confined in a one dimensional box, the scalar particle with linear vector and scalar potentials and the case of inversely linear vector and scalar potentials of Coulomb-type. The expressions of bound state energies and the associated wave functions are exactly determined for these three cases.

中文翻译：

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新型扩展不确定性原理中的标量粒子

在使用位移算子方法的新型扩展不确定性原理的背景下，我们提出了一些问题的精确解，例如：限制在一维盒子中的 Klein-Gordon 粒子，具有线性向量和标量势的标量粒子和逆线性向量和库仑型标量势的情况。对于这三种情况，束缚态能量和相关波函数的表达式是精确确定的。