广义Delta函数及其在量子光学中的应用
Generalized Delta Functions and Their Use in Quantum Optics
摘要：
狄拉克δ函数在物理学和数学的许多领域都有广泛的应用。在这里，我们考虑一个狄拉克δ函数的推广，允许使用复杂的参数。我们表明，广义δ函数的性质是非常不同的狄拉克δ函数，他们的行为更像一个极点在复平面。我们使用广义δ函数导出了薛定谔猫态的Glauber-Sudarshan P-函数，其形式非常简单。除了它们在经典电磁学和量子光学中的潜在应用之外，这些结果还提供了对角P函数描述具有非对角元素的密度算子的能力。
英文摘要：
The Dirac delta function is widely used in many areas of physics and mathematics. Here we consider the generalization of a Dirac delta function to allow the use of complex arguments. We show that the properties of a generalized delta function are very different from those of a Dirac delta function and that they behave more like a pole in the complex plane. We use the generalized delta function to derive the Glauber-Sudarshan P-function for a Schrödinger cat state in a surprisingly simple form. Aside from their potential applications in classical electromagnetism and quantum optics, these results provide insight into the ability of the diagonal P-function to describe density operators with off-diagonal elements.
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