Скачать или смотреть S-1 Problems on acceptable wave function

An acceptable wave function in quantum mechanics must satisfy a few key conditions to correctly describe a real physical system. First, it must be single-valued, meaning it can have only one value at any given point in space and time so, that probability is well defined. The wave function must also be finite everywhere, because infinite values would lead to impossible physical results. It should be continuous and smooth, and its first derivative must also be continuous, except at points where the potential energy becomes infinite. Another important condition is that the wave function must be square-integrable, which allows it to be normalized so the total probability of finding the particle is equal to one. Finally, for bound systems, the wave function must approach zero as we move far away from the region of interest, ensuring the particle remains confined. These conditions together make sure that the wave function represents a physically meaningful and measurable state.
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