# Why is the word amplitude used in quantum computing?

Apparently no one has asked why the word "amplitude" is used to refer to the complex numbers that determine the probability of a quantum object to be found in a certain state. The word amplitude to me means the distance between the lowest point on a graph and the highest point. But I don't know how to apply this use of the word to the amplitudes of a quantum object. Can you explain? I've been looking at various books and I suspect everyone just assumes the meaning is clear somehow because nobody seems to explain. If you could cite a source, that would be even more helpful. Thank you.

• Possible line of reasoning: 1) A wavefunction looks like a wave 2) waves have amplitudes 3) finite-dimensional quantum states are kind of like discrete wavefunctions therefore 4) numbers describing quantum states are called amplitudes Nov 10, 2023 at 1:57

Sine waves, such as AC signals or water waves or electromagnetic waves, are fully characterized in terms of their phase relative to time $$t_0$$ as well as their amplitudes, which, as you describe, is the difference between the maximum and the minimum. But certainly electrical engineers are familiar with Euler's formula relating sines and cosines to the exponential function - and they call the amplitudes the coefficient in front of the exponent. Schrödinger wrote down his equation, and saw that it was a wave equation - as @forky40 says it's a natural consequence to call the coefficients amplitudes.