PROBABILITY AMPLITUDE
The first general principle of the quantum mechanics lies in the following: the probability of the fact that a particle coming out of source s will achieve point x, can be presented numerically by square absolute value of a complex number, which is called probability amplitude. To designate probability amplitude a shorthand symbol <x|s> is used.
According to the second general principle of quantum mechanics, if a particle can achieve state x by one of two possible ways, then the complete amplitude of the process is the sum of amplitudes for these two ways, viewed separately:
According to the third general principle of quantum mechanics, when a particle goes by a certain given way, then amplitude for this way can be presented as a product of the amplitude of passing a part of the way (up to point a) by the amplitude of passing the rest of the way: <x|s> = <x|a>·<a|s>.