论文标题
Dirac的谐波振荡器的经典量词类比：热辐射中的经典方面包括零点辐射
Dirac's Classical-Quantum Analogy for the Harmonic Oscillator: Classical Aspects in Thermal Radiation Including Zero-Point Radiation
论文作者
论文摘要
DIRAC的泊松支架 - 托架到交通剂类比，从经典机制到量子力学的过渡确保，对于许多系统，经典和量子系统具有相同的代数结构。类比的量子侧（涉及希尔伯特空间上的运算符，并以普朗克的常数$ \ hbar $缩放的换向器）不仅给出了代数结构，而且还决定了量子基态下物理量的平均值。另一方面，仅提供经典规范转换的非依赖性力学的泊松支架不会给出任何物理量的值。相反，必须走出非同性主义的经典力学，以便获得经典物理学的基本相空间分布。我们假设在任何温度下，经典理论中的物理量值取决于相位空间概率分布，该分布由热辐射平衡产生，包括经典的零点辐射，其比例由普朗克的常数$ \ hbar $设置。热辐射中的所有机械系统都将从热辐射中继承常数$ \ hbar $。在这里，我们注意到一个和三个空间维度的谐波振荡器的所有温度的经典理论和量子理论（一致性和对比度）之间的联系。
Dirac's Poisson-bracket-to-commutator analogy for the transition from classical to quantum mechanics assures that for many systems, the classical and quantum systems share the same algebraic structure. The quantum side of the analogy (involving operators on Hilbert space with commutators scaled by Planck's constant $\hbar$) not only gives the algebraic structure but also dictates the average values of physical quantities in the quantum ground state. On the other hand, the Poisson brackets of nonrelativistic mechanics, which give only the classical canonical transformations, do not give any values for physical quantities. Rather, one must go outside nonrelativistic classical mechanics in order to obtain a fundamental phase space distribution for classical physics. We assume that the values of physical quantities in classical theory at any temperature depend on the phase space probability distribution which arises from thermal radiation equilibrium including classical zero-point radiation with the scale set by Planck's constant $\hbar$. All mechanical systems in thermal radiation will inherit the constant $\hbar$ from thermal radiation. Here we note the connections between classical and quantum theories (agreement and contrasts) at all temperatures for the harmonic oscillator in one and three spatial dimensions.
