degenerate

Examples of degenerate in the following topics:

• The Third Law of Thermodynamics and Absolute Energy

  • An example of a system which does not have a unique ground state is one containing half-integer spins, for which there are two degenerate ground states.
  • In addition, glasses and solid solutions retain large entropy at absolute zero, because they are large collections of nearly degenerate states, in which they become trapped out of equilibrium.
  • Materials that remain paramagnetic at absolute zero, by contrast, may have many nearly-degenerate ground states, as in a spin glass, or may retain dynamic disorder, as is the case in a spin liquid.

• Octahedral Complexes

  • For a free ion, such as gaseous Ni2+ or Mo, the d orbitals are degenerate.

• Wave Equation for the Hydrogen Atom

  • For the hydrogen atom, states of the same n but different ℓ are also degenerate (they have the same energy).
  • Explain how the solution of the Schrödinger equation for the hydrogen atom yields the four quantum numbers and use these to identify degenerate states

• Crystal Field Theory

  • In most cases, the d orbitals are degenerate, but sometimes they can split, with the eg and t2g subsets having different energy.

• Reactions of Coordination Compounds

  • One important indicator of reactivity is the rate of degenerate exchange of ligands.

• Sigmatropic Rearrangements

  • The degenerate or self-replicating Cope rearrangement has been a fascinating subject of research.

• Description of the Hydrogen Atom

  • In addition, for the hydrogen atom, states of the same n but different ℓ are also degenerate (i.e. they have the same energy).

• Properties of Oxygen

  • The electron configuration of the molecule has two unpaired electrons occupying two degenerate molecular orbitals.

• Semiconductors

  • When a semiconductor is doped to such a high level that it acts more like a conductor than a semiconductor, it is referred to as degenerate.

• Hund's Rule

  • Although the implications are clear for orbitals of different principal quantum number (n), which are clearly of different energy, the filling order is less clear for degenerate sublevels.