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Wave Function Constraints and Normalization
In quantum mechanics, the wave function tells you everything you need to know about the motion and behavior of a system. However, in order for the wave function to give you a physically meaningful and measurable probability value, the wave function must satisfy a certain set of requirements. Firstly, the wave function must be a solution to the Schrodinger equation. Secondly, the wave function must be a continuous function (if the square of the absolute value of the wave function is to give you an actual probability, the wave function cannot be discontinuous anywhere). And thirdly, the wave function must be normalized. What exactly does this mean? Well, for the wave function to give us a correct probability value, we must make sure the probably never exceeds 1. Put another way, the probability of find an electron in one place or another should always be equal to 1 (or 100%).
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