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The Schrodinger equation is for when you want to find what energy levels are allowed. The wave function provides the probability of finding the particle at a specific position. It is not responsible for shapes in an atom.
The Schrodinger equation is used to derive the quantum numbers, which elucidate the shapes of the atoms. For instance, the square of the wave function that comes from the Schrodinger equation tells us the probability density of the elections, which informs us on the shape of the atomic orbitals.
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