叠加的必要条件

On the Necessary Conditions of Superposition

论述了叠加的必要条件并对叠加和累加作了区分。叠加的必要条件是参与运算的物理量同时存在于同一地点并且具有同一性质。参与运算的物理量满足同一性质但不满足同时性条件或同地性条件的相加或者属于不同质点的物理量的相加为累加。叠加必然满足交换律,累加则不一定满足交换律。在经典力学中,叠加是关于单个质点的物理量的相加,关于多个质点的物理量的相加必然不是叠加;累加则不一定是关于单个质点的物理量的相加。论文对于叠加原理的理解和运用具有非常重要的意义。

There are two kinds of addition, namely, superposition and accumulation. Superposition is the kind of addition that the addendums are simultaneous and at the same point and have the same property. Accumulation is the kind of addition that the adden- dums are not simultaneous or not at the same point. The commutative law holds for superposition without exception, but it does not necessarily for accumulation. In classic mechanics, the addendums of superposition are all about a single particle, the addition whose addendums are about different particles is not superposition unexceptionally; while the addendums of accumulation are not necessarily about a single particle. The article is very important in understanding and using the superposition principle.