论文标题
广义扩展动量操作员
Generalized Extended Momentum Operator
论文作者
论文摘要
我们研究并概括满足扩展不确定性原理关系（EUP）的动量操作员。这种广义的扩展动量运算符（GEMO）由位置运算符的任意辅助功能，$μ\ left（x \ right）$组成，以使Gemo不仅满足EUP关系，而且是Hermitian。接下来，我们将GEMO应用于构建广义的一维Schrödinger方程。使用所谓的点规范变换（PCT）后，我们将广义的schrödinger方程式从$ x $ - 空间转换为$ z $ - 空间，在转换的坐标中，$ z $，它是schrödinger方程的标准形式。在继续，我们研究了两个说明性示例，并在分析上求解相应的方程以找到能量谱。
We study and generalize the momentum operator satisfying the extended uncertainty principle relation (EUP). This generalized extended momentum operator (GEMO) consists of an arbitrary auxiliary function of position operator, $μ\left( x\right) $, in such a combination that not only GEMO satisfies the EUP relation but also it is Hermitian. Next, we apply the GEMO to construct the generalized one-dimensional Schrödinger equation. Upon using the so called point canonical transformation (PCT), we transform the generalized Schrödinger equation from $x$-space to $z$-space where in terms of the transformed coordinate, $z$, it is of the standard form of the Schrödinger equation. In continuation, we study two illustrative examples and solve the corresponding equations analytically to find the energy spectrum.
