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The number of different states corresponding to a particular energy level is known as the degree of degeneracy (or simply the degeneracy) of the level. It is represented mathematically by the Hamiltonian for the system having more than one linearly independent eigenstate with the same energy eigenvalue.
Degenerate zeroth-order states of opposite parity occur for excited hydrogen-like (one-electron) atoms or Rydberg states. Neglecting fine-structure effects, such a state with the principal quantum number n is n 2 -fold degenerate and n 2 = ∑ ℓ = 0 n − 1 ( 2 ℓ + 1 ) , {\displaystyle n^{2}=\sum _{\ell =0}^{n-1}(2\ell +1),} where ℓ ...
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.
The role of excited states in softening the ground state with respect to distortions in benzene was demonstrated qualitatively by Longuet-Higgins and Salem [6] by analyzing the π electron levels in the Hückel approximation, while a general second-order perturbation formula for such vibronic softening was derived by Bader in 1960. [7]
The ground state of a quantum-mechanical system is its stationary state of lowest energy; 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. In quantum field theory, the ground state is usually called the vacuum state or the vacuum.
When S > L there are only 2L+1 orientations of total angular momentum possible, ranging from S+L to S-L. [2] [3] The ground state of the nitrogen atom is a 4 S state, for which 2S + 1 = 4 in a quartet state, S = 3/2 due to three unpaired electrons. For an S state, L = 0 so that J can only be 3/2 and there is only one level even though the ...
For example, the hydrogen (H) atom contains one proton and one electron, so that the Kramers theorem does not apply. Indeed, the lowest (hyperfine) energy level of H is nondegenerate, although a generic system might have degeneracy for other reasons.
Atoms can be excited by heat, electricity, or light. The hydrogen atom provides a simple example of this concept.. The ground state of the hydrogen atom has the atom's single electron in the lowest possible orbital (that is, the spherically symmetric "1s" wave function, which, so far, has been demonstrated to have the lowest possible quantum numbers).