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Can there be multiple ground states?

  1. Mar 25, 2014 #1
    I am reading an article on wikipedia about ground state and it says -


    The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. The ground state of a quantum field theory is usually called the vacuum state or the vacuum.

    If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state and commutes with the Hamiltonian of the system.

    I am confused about what it says there at the beginning of the second paragraph, that "If more than one ground state exists, they are said to be degenerate". It says in the paragraph before that the ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero point energy of the system. How could there possibly be two ground states?????????
     
  2. jcsd
  3. Mar 25, 2014 #2
    Take two electrons in an orbital. One must be spin up, one must be spin down.
    Use lower case for down, upper case for UP. call the electrons a and b. aB and Ab are two degenerate configurations of equivalent energy. There are dozens of other simple examples of degeneracy I can think of off the top of my head, but this should do. Another is picture a crystal lattice. Say you have a mole of atoms in the crystal. Now, at a given temperature there will be a certain number of defects present (where one atom is "off lattice"). Say this is the "ground state". How many different possibilities are there for a 6E23 atoms in a lattice with just one off lattice? How many with 2? With 3, 4, ...100, 1000000,....
     
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