Search results
Results from the WOW.Com Content Network
Examples of two-state systems in which the degeneracy in energy states is broken by the presence of off-diagonal terms in the Hamiltonian resulting from an internal interaction due to an inherent property of the system include: Benzene, with two possible dispositions of the three double bonds between neighbouring Carbon atoms.
While degeneracy pressure usually dominates at extremely high densities, it is the ratio between degenerate pressure and thermal pressure which determines degeneracy. Given a sufficiently drastic increase in temperature (such as during a red giant star's helium flash ), matter can become non-degenerate without reducing its density.
Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state and 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.
In quantum mechanics terminology, the degeneracy is said to be "lifted" by the presence of the magnetic field. In the presence of more than one unpaired electron, the electrons mutually interact to give rise to two or more energy states. Zero-field splitting refers to this lifting of degeneracy even in the absence of a magnetic field.
More generally, condensation refers to the appearance of macroscopic occupation of one or several states: for example, in BCS theory, a superconductor is a condensate of Cooper pairs. [1] As such, condensation can be associated with phase transition , and the macroscopic occupation of the state is the order parameter .
This degeneracy is lifted when spin–orbit interaction is treated to higher order in perturbation theory, but still states with same |M S | are degenerate in a non-rotating molecule. We can speak of a 5 Σ 2 substate, a 5 Σ 1 substate or a 5 Σ 0 substate. Except for the case Ω = 0, these substates have a degeneracy of 2.
In the case of degenerate energy levels, we can write the partition function in terms of the contribution from energy levels (indexed by j) as follows: =, where g j is the degeneracy factor, or number of quantum states s that have the same energy level defined by E j = E s.
is the degeneracy of energy level i, that is, the number of states with energy which may nevertheless be distinguished from each other by some other means, [nb 1] μ is the chemical potential, k is the Boltzmann constant, T is absolute temperature,