All Topics  
Degenerate energy level

 

 
   Email Print
   Bookmark   Link
 

 

Degenerate energy level
 
 
  Topics Degenerate energy level Topic Home

In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 two or more different physical states are said to be degenerate if they are all at the same energy level
Energy level

A Quantum mechanics system or particle that is Bound state, confined spatially, can only take on certain discrete values of energy, as opposed to Classical mechanics particles, which can have any energy....
. Physical states differ if and only if they are linearly independent. An energy level is said to be degenerate if it contains two or more different states. The number of different states at a particular energy level is called the level's degeneracy.

In quantum theory
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 this usually pertains to electronic configurations and the electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
's energy levels, where different possible occupation states for particles may be related by symmetry
Symmetry

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance; such that it reflects beauty or perfection....
.






Discussion
Ask a question about 'Degenerate energy level'
Start a new discussion about 'Degenerate energy level'
Answer questions from other users
Full Discussion Forum



Encyclopedia


In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 two or more different physical states are said to be degenerate if they are all at the same energy level
Energy level

A Quantum mechanics system or particle that is Bound state, confined spatially, can only take on certain discrete values of energy, as opposed to Classical mechanics particles, which can have any energy....
. Physical states differ if and only if they are linearly independent. An energy level is said to be degenerate if it contains two or more different states. The number of different states at a particular energy level is called the level's degeneracy.

In quantum theory
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 this usually pertains to electronic configurations and the electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
's energy levels, where different possible occupation states for particles may be related by symmetry
Symmetry

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance; such that it reflects beauty or perfection....
. For example, in the Bohr model
Bohr model

In atomic physics, the Bohr model created by Niels Bohr depicts the atom as a small, positively charged atomic nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction, rather than gravity....
 of the hydrogen atom
Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen. The Electric charge neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force....
, all of the states with the same angular momentum (which corresponds to them having the same principal quantum number
Principal quantum number

In atomic physics, the principal quantum number symbolized as n is the firstof a set of quantum numbers of an atomic orbital. The quantum number n labels the energy levels of hydrogenic atoms....
) are degenerate. The usage comes from the fact that degenerate eigenstates correspond to identical eigenvalues of the Hamiltonian
Hamiltonian

Hamiltonian may refer toIn mathematics:* Hamiltonian system* Hamiltonian path, in graph theory* Hamiltonian group, in group theory* Hamiltonian ...
. Since eigenvalues correspond to roots of the characteristic equation, degeneracy here has the same meaning as the common mathematical usage of the word.

If the symmetry is broken by a perturbation, caused, for example, by applying an external electric field
Electric field

In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field ....
, the energies of the states can be changed, causing energy level splitting
Energy level splitting

Energy level splitting occurs in physics when the degenerate energy levels of two or more states are split because of external fields or other effects....
.

In electromagnetics
Electromagnetic radiation

Electromagnetic radiation takes the form of wave propagation waves in a vacuum or in matter. EM radiation has an electric field and magnetic field component which oscillate in phase perpendicular to each other and to the direction of energy Wave propagation....
, degeneracy refers to modes of propagation which exist at the same frequency and longitudinal propagation constant. As an example, for a rectangular waveguide
Waveguide (electromagnetism)

In electromagnetics and communications system engineering, the term waveguide may refer to any linear structure that guides electromagnetic waves....
, the TEmn mode is degenerate to the TMmn mode if m and n are the same for both of them.

See also

  • Density of states
    Density of states

    In statistical physics and condensed matter physics, the density of states of a system describes the number of states at each energy level that are available to be occupied....