schrodinger equation and orbitals

[Emerson Gaspar 1D]

could someone explain how the schrodinger equation is related to atomic orbitals? I'm going over the objective saying to "Understand the relationship between Schrodinger's equation, wave function, and orbitals" and I understand how it relates to wave functions but not to orbitals.

[Aisah_Akbar_2C]

okay so basically the schrodinger euqraion helps us understand where electrons are likely to be around on atom which gives us solutions called wave functions (maps showing probable locations of electrons) and when thee maps are squares they give us the likelihood of finding an electron in a specific space - aka atomic orbiatsl. we just figuring out the shapes and regions where electrons are around the atom

[Levy Shaked]

Agreed. To go a bit more in depth, a wave function for a point in space represents the amplitude of the energetic oscillation occurring at that point (as an electron behaves as a standing wave where each point in space undergoes simple harmonic oscillation). The square of the wave function at a point, however, describes the likelihood for finding the electron as a particle at that point. This makes sense, because wave functions often have negative values and a probability cannot be negative, so squaring it eliminates this probability; moreover, points with greater amplitudes of oscillation for the wave-model of the electron are more likely to contain an electron particle at any given time. There are some points, however, where the square of the radial or angular wave function equals zero; these points make up radial and angular nodes in the shapes of orbitals. At a value where the radial wave function equals zero, an electron has a zero chance of occurring at that distance from the nucleus at any orientation in space, forming an empty sphere shape at that distance. At a value where the angular wave function equals zero, an electron has zero chance of occurring at that latitude and longitude for any radial distance, either positive or negative, from the nucleus, forming an empty plane shape at that lat/long. The number and locations of radial and angular nodes, which are determined by the zeros of the radial and angular wave functions, thus determine the shape of an orbital.