Fock-Bargmann量子态表示中的流体力学镜像法与量子微积分
Method of Hydrodynamic Images and Quantum Calculus in Fock-Bargmann Representation of Quantum States
AI总结：
本文提出用经典流体力学描述Fock空间量子态，将波函数零点视为点涡镜像，并用Jackson q-指数函数刻画q-变形相干态。
摘要：
我们提出一种以经典流体力学描述Fock空间中量子态的新方法。通过对表示Fock-Bargmann表示中量子态波函数的复解析函数进行共形映射，我们定义了复势，用以描述这些量子态的不可压缩无旋经典流体力学流动。在我们的方法中，波函数的零点表现为平面上一组强度相同的点涡（源），从而可以将它们解释为有界区域中的镜像。对于猫态，我们发现其流体表示可描述为斜条形区域中的一个点源，具有无限多个周期性分布的镜像。对于环形区域，无限镜像集合由Jackson q-指数函数描述。我们证明这些函数表示q-变形量子振子的量子相干态在q-Fock-Bargmann表示中的波函数，并描述按几何级数分布的无限点涡集合。
英文摘要：
We propose a new approach to quantum states in Fock space in terms of classical hydrodynamics. By conformal mapping of complex analytic function, representing the wave function of quantum states in Fock-Bargmann representation, we define the complex potential, describing these quantum states by incompressible and irrotational classical hydrodynamic flow. In our approach, zeros of the wave function appear as a set of point vortices (sources) in plane with the same strength, allowing interpretation of them as images in a bounded domain. For the cat states we find fluid representation as descriptive of a point source in the oblique strip domain, with infinite number of periodically distributed images. For the annular domain, the infinite set of images is described by Jackson $q$-exponential functions. We show that these functions represent the wave functions of quantum coherent states of the $q$-deformed quantum oscillator in q-Fock-Bargmann representation and describe the infinite set of point vortices, distributed in geometric progression.
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