- published: 04 Dec 2012
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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. It turns out that degeneracy occurs whenever a nontrivial unitary operator commutes with the Hamiltonian of the system.
According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero because the logarithm of 1 is 0. It is also possible for the highest excited state to have absolute zero temperature for systems that exhibit negative temperature.
Carrie Marie Underwood (born March 10, 1983) is an American country singer, songwriter and actress who rose to fame as the winner of the fourth season of American Idol, in 2005. Underwood has since become a multi-platinum selling recording artist, a winner of several Grammy Awards, Billboard Music Awards and American Music Awards, a Golden Globe Award nominee, a three-time Academy of Country Music and Country Music Association Female Vocalist winner, and a two-time ACM Entertainer of the Year. She is the first-ever female artist to win back-to-back Academy of Country Music (ACM) Awards for Entertainer of the Year (2009/10). Underwood was inducted into and became a member of the Grand Ole Opry in 2008. She was also inducted into the Oklahoma Music Hall of Fame in 2009.Billboard named Underwood Country Music's reigning Queen in 2012.
Willie Hugh Nelson (pronounced /wɪli nɛlsən /; born April 30, 1933) is an American country music singer-songwriter, as well as an author, poet, actor, and activist. The critical success of the album Shotgun Willie (1973), combined with the critical and commercial success of Red Headed Stranger (1975) and Stardust (1978), made Nelson one of the most recognized artists in country music. He was one of the main figures of outlaw country, a subgenre of country music that developed at the end of the 1960s as a reaction to the conservative restrictions of the Nashville sound. Nelson has acted in over 30 films, co-authored several books, and has been involved in activism for the use of biofuels and the legalization of marijuana.