Linear Combinations of p Orbitals

The real forms of atomic orbitals are constructed by taking appropriate linear combinations of the complex forms of these orbitals. The one-electron wavefunctions resulting from the solution of the Schrödinger equation for the hydrogen atom are complex functions except when . Boundary surface pictures of atomic orbitals typically only show the real part of these complex functions and often leave out the sign information as well. Here, boundary surfaces of the orbitals are drawn with coloring to indicate the real and imaginary components as well as the positive and negative signs. These color-coded atomic orbitals illustrate the linear combinations of the complex wavefunctions that produce the familiar and orbitals.

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