# Linear Combinations of f Orbitals

Linear Combinations of f Orbitals

It is less common to find the atomic orbitals illustrated in chemistry textbooks than the , , and orbitals. Boundary surface pictures of any of these atomic orbitals typically only show the real part of these complex functions and often leave out the sign information as well. The one-electron wavefunctions resulting from the solution of the Schrödinger equation for the hydrogen atom are complex functions except when =0. The real forms of atomic orbitals can be constructed by taking appropriate linear combinations of the complex forms. Here, boundary surfaces of the orbitals are colored to indicate the real and imaginary components as well as the positive and negative signs.

f

s

p

d

m

ℓ

f

f