The requirement that the waves must be in phase with one another to avoid cancellation and produce a standing wave results in a limited number of solutions (wavefunctions), each of which is specified by a set of numbers called quantum numbers. Schrödinger incorporated Legendre’s equations into his wavefunctions. states that electrons can only exist at specific distances from the nucleus. This model, which is the basis of the modern understanding of the atom, is known as the quantum mechanical or wave mechanical model. predicts the specific location of the electron in an atom. You will see very quickly they are quite different from the Bohr model. I would recommend reading about atomic orbitals, the Wikipedia page is quite interesting. Instead electrons are quite different, they are spread out a bit like clouds of gas, in areas called atomic orbitals. Fortunately, however, in the 18th century, a French mathematician, Adrien Legendre (1752–1783), developed a set of equations to describe the motion of tidal waves on the surface of a flooded planet. The quantum mechanical model of the atom differs from the Bohr model in that it A. The quantum model does not have electron trajectories. From the patterns of one- and two-dimensional standing waves shown previously, you might expect (correctly) that the patterns of three-dimensional standing waves would be complex.
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