As I understand it, quantum mechanics for particles was developed to replace classical mechanics for particles. In essence, we realized that particle cannot be given an exact place and momentum but must be described using probabilities and more specifically wave functions.
Is quantizing a field the same idea? That is, suppose I am considering an electric field $\mathbf E(\mathbf x,t)$. Does quantizing a field mean that we no longer believe the field can have a definite value at points in spacetime? Does this mean we are looking to find a wave function analogue for fields?
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