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(quantum mechanics, physical chemistry) A mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus.

The shapes of the first five atomic orbitals are 1s, 2s, 2p_x, 2p_y, and 2p_z. The two colors show the phase or sign of the wave function in each region. Each picture is domain coloring of a ψ(x, y, z) function which depends on the coordinates of one electron. To see the elongated shape of ψ(x, y, z)² functions that show probability density more directly, see pictures of d-orbitals below.

The physical region or space where an electron can be calculated to be present, as defined by the particular mathematical form of the orbital.

Cross-sections of atomic orbitals of the electron in a hydrogen atom at different energy levels. The probability of finding the electron is given by the color, as shown in the key at upper right.

(quantum mechanics, physical chemistry) A mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus.

3D views of some hydrogen-like atomic orbitals showing probability density and phase (g orbitals and higher not shown)