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The Schrodinger equation provides the definite energy space an electron can occupy inside a shell in the atom. The wave function, one of its variables, actually gives the probable location of an electron in space.


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It probably depends what interpretation of quantum physics you subscribe to. That sounds approximately right for the Copenhagen interpretation, in which you aren't allowed to analyze where the wave function comes from. For those who appreciate more what de Broglie, Einstein, Bell and others have put into quantum physics, there's always the interpretation ...


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It's unnecessary to check it for particular functional forms. After all, the functional forms aren't exact. In particular, it's not true that the intensity at all interference minima is strictly zero. The minima away from the center of the picture are closer to one of the slits, so the wave function from the slit is larger (in absolute value), and therefore ...



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