矩阵力学与波动力学等价性证明的历史分析

矩阵力学和波动力学是量子力学的两种早期形态。前者由海森堡、约当、玻恩提出,后者由薛定谔提出。1926年,薛定谔给出二者之间等价性的证明。随后,泡利、狄拉克、约当、冯·诺伊曼等人或是为等价性证明给出新的版本,或是给出了间接的论证。这两种力学现在已被表述为海森堡绘景和薛定谔绘景,而数学家近来又从量子化问题出发对其等价性做出新的考察。本文对此历史过程进行回顾分析,以评估等价性问题对物理发展的意义。

An Analysis of the History of Proof of Equivalence Between Matrix Mechanics and Wave Mechanics

Matrix mechanics and wave mechanics are two early formulations of quantum mechanics.The former was put forward by Heisenberg,Jordan and Born,and the latter by Schr?dinger.In 1926,Schr?dinger proved the equivalence between the two formulations,and then Pauli,Dirac,Jordan,Von Neumann had either given new versions of proofs,or provided indirect arguments.These two formulations are now presented as Heisenberg picture and Schr?dinger picture,but recently mathematicians have made new progress on their equivalence in the light of the quantization problem.This paper examines and analyses this historical course to estimate the significance of the equivalence problem in the development of physics.