在量子力学里，机率幅，又称为量子幅，是一个描述粒子的量子行为的复函数。例如，机率幅可以描述粒子的位置。当描述粒子的位置时，机率幅是一个波函数，表达为位置的函数。这波函数必须符合薛丁格方程。

一个机率幅的机率密度函数是 ，等于 ，又称为机率密度。在使用前，不一定要将机率密度函数归一化。尚未归一化的机率密度函数可以给出关于机率的相对大小的信息。

假若，在整个三维空间内，机率密度 是一个有限积分。那么，可以计算一个归一常数 ，替代 为 ，使得有限积分等于1。这样，就可以将机率幅归一化。粒子存在于某一个特定区域内的机率是 在区域的积分。这句话的含义是，根据量子力学的哥本哈根诠释，假若，某一位观察者试着测量这粒子的位置。他找到粒子在 区域内的机率 是

In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.

Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see References), and the probability thus calculated is sometimes called the "Born probability". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.