Can someone give me a clear explanation of what is the difference between a classical field, a wave function of a particle and a quantum field? I haven't find a clear explanation. For example for Klein-Gordon equation, the solution $\phi(x)$ is a plane wave, but $\phi(x)$ can be interpreted in any of the 3 ways I mentioned above and I am not sure what is the difference between them. (for example I am not sure why the wave function is not a field, as it assigns to any point in space a value, so it seems to behave like a field). Thank you!
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