80 Years of Professor Wigner's Seminal Work "On Unitary Representations of the Inhomogeneous Lorentz Group"
80 Years of Professor Wigner's Seminal Work "On Unitary Representations of the Inhomogeneous Lorentz Group"
复制标题
DOI：
10.2307/1968551
复制
发表时间：
2021-11
影响因子：
4.9
通讯作者：
E. Wigner
中科院分区：
文献类型：
--
作者：
E. Wigner
量子力学最基本的原理可能是态系统形成一个线性流形，其中定义了一个酉标积。态通常由波函数表示，φ和φ的常数倍数表示相同的物理状态。因此，可以将波函数归一化，即，将其乘以常数因子，使得其与自身的标积变为1。然后，只有一个模为1的常数因子，即所谓的相位，在波函数中是不确定的。波函数的线性特征称为叠加原理。两个归一化波函数的幺正标积（λ，Φ）的模的平方称为从态λ到Φ的跃迁概率，反之亦然。这是为了给出一个概率，即在一个处于状态Φ的系统上进行实验，看看这个状态是否是π，结果是π。如果有两个或多个不同的实验来决定这一点（例如，基本上相同的实验，在不同的时间进行）它们都应该给出相同的结果，即，转移概率具有不变的物理意义。
It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally represented by wave functions3 in such a way that φ and constant multiples of φ represent the same physical state. It is possible, therefore, to normalize the wave function, i.e., to multiply it by a constant factor such that its scalar product with itself becomes 1. Then, only a constant factor of modulus 1, the so-called phase, will be left undetermined in the wave function. The linear character of the wave function is called the superposition principle. The square of the modulus of the unitary scalar product (ψ,Φ) of two normalized wave functions ψ and Φ is called the transition probability from the state ψ into Φ, or conversely. This is supposed to give the probability that an experiment performed on a system in the state Φ, to see whether or not the state is ψ, gives the result that it is ψ. If there are two or more different experiments to decide this (e.g., essentially the same experiment, performed at different times) they are all supposed to give the same result, i.e., the transition probability has an invariant physical sense.