Symmetric wave functions are not governed by this principle, but the anti-symmetric wave functions of spin one-half particles are.  
This principle is invoked in a term in the Weizsaecker Formula for determining the binding energy of nuclei, and the related liquid drop model utilizes a consequence of this that favors nuclei with even numbers of protons and neutrons.  It explains the formation of neutron stars through degeneracy, and it leads to the formation of a "Fermi sea" at absolute zero.  Symmetric wave functions are not governed by this principle, but the anti-symmetric wave functions of spin one-half particles are.  FTP name this principle that says no two fermions can occupy the same quantum state simultaneously.
This principle is invoked in a term in the Weizsaecker Formula for determining the binding energy of nuclei, and the related liquid drop model utilizes a consequence of this that favors nuclei with even numbers of protons and neutrons.  
Pauli exclusion principle