论文标题
$ \ Mathcal {pt} $ - 对称概括性扩展动量运算符
$\mathcal{PT}$-Symmetric Generalized Extended Momentum Operator
论文作者
论文摘要
我们进一步开发了广义扩展动量运算符（GEMO）的概念，该概念是在最近在\ citep {m.h2}中引入的，并提出了所谓的$ \ Mathcal {pt} $ - 对称的gemo。与Gemo类似，$ \ Mathcal {pt} $ - 对称的Gemo也满足了扩展的不确定性原理（EUP）关系。此外，在$ \ Mathcal {pt} $ - 对称的gemo上构建的相应哈密顿量，具有真实或$ \ Mathcal {pt} $ - 对称的潜力，仍然是非Hermitian，但$ \ Mathcal {pt} $ - 对称性 - 对称性 - 对称性，因此其能量和动量和动量和动量是真实的。我们将形式主义应用于无准量子粒子，并提出了能量光谱的精确溶液。
We develop further the concept of generalized extended momentum operator (GEMO), which has been introduced very recently in \citep{M.H2}, and propose the so called $\mathcal{PT}$-symmetric GEMO. In analogy with GEMO, the $\mathcal{PT}$-symmetric GEMO also satisfies the extended uncertainty principle (EUP) relation. Moreover, the corresponding Hamiltonian that is constructed upon the $\mathcal{PT}$-symmetric GEMO, with a real or $\mathcal{PT}$-symmetric potential, remains non-Hermitian but $\mathcal{PT}$-symmetric and consequently its energy and momentum eigenvalues are real. We apply our formalism to a quasi-free quantum particle and the exact solutions for the energy spectrum are presented.
