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Final answer:
Schrödinger's work on the quantum model of the atom required an understanding of quantum mechanics and wave-particle duality.
Explanation:
The scientific knowledge necessary for Schrödinger's work on the quantum model of the atom was the development of quantum theory. Quantum mechanics, introduced by physicists like Schrödinger and Heisenberg, revolutionized the understanding of the behavior of subatomic particles, treating them as having wave-particle duality.
In 1925, Schrödinger and Heisenberg independently introduced mathematically different but equivalent formulations of quantum mechanics, attributing wave properties to electrons. This shift from classical mechanics to quantum mechanics was essential for Schrödinger's development of the quantum model of the atom.
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