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In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system.Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement.
Molecular orbitals are said to be degenerate if they have the same energy. For example, in the homonuclear diatomic molecules of the first ten elements, the molecular orbitals derived from the p x and the p y atomic orbitals result in two degenerate bonding orbitals (of low energy) and two degenerate antibonding orbitals (of high energy). [13]
Each Landau level is degenerate because of the second quantum number , which can take the values =, where is an integer. The allowed values of N {\displaystyle N} are further restricted by the condition that the center of force of the oscillator, x 0 {\displaystyle x_{0}} , must physically lie within the system, 0 ≤ x 0 < L x {\displaystyle 0 ...
See illustration of a cross-section of these nested shells, at right. The s orbitals for all n numbers are the only orbitals with an anti-node (a region of high wave function density) at the center of the nucleus. All other orbitals (p, d, f, etc.) have angular momentum, and thus avoid the nucleus (having a wave node at the nucleus).
Octahedral crystal field stabilization energy. Degenerate atomic d-orbitals of a free metal ion (left), destabilization of d-orbitals within a spherical negative electric field (center), and loss of degeneracy relative to the spherical field when ligands are treated as point charges in an octahedral geometry.
When creating the molecular orbitals from the p orbitals, the three atomic orbitals split into three molecular orbitals, a singly degenerate σ and a doubly degenerate π orbital. Another property we can observe by examining molecular orbital diagrams is the magnetic property of diamagnetic or paramagnetic. If all the electrons are paired ...
The multiplicity is often equal to the number of possible orientations of the total spin [3] relative to the total orbital angular momentum L, and therefore to the number of near–degenerate levels that differ only in their spin–orbit interaction energy. For example, the ground state of a carbon atom is 3 P (Term symbol).
The valence orbitals of molecular oxygen (middle); in the ground state, the electrons in the π* orbitals have their spins parallel. The s = 1 ⁄ 2 spins of the two electrons in degenerate orbitals gives rise to 2 × 2 = 4 independent spin states in total.