Density of states

<p>In <a href="/facts/Condensed_matter_physics/EBVI5nmL">condensed matter physics</a>, the density of states (DOS) of a system describes the number of allowed modes or <a href="/facts/Quantum_state/7jbxd7Dx">states</a> per unit energy range. The density of states is defined as 
  
    
      
        D
        (
        E
        )
        =
        N
        (
        E
        )
        
          /
        
        V
      
    
    {\displaystyle D(E)=N(E)/V}
  
, where 
  
    
      
        N
        (
        E
        )
        δ
        E
      
    
    {\displaystyle N(E)\delta E}
  
 is the number of states in the system of volume 
  
    
      
        V
      
    
    {\displaystyle V}
  
 whose energies lie in the range from 
  
    
      
        E
      
    
    {\displaystyle E}
  
 to 
  
    
      
        E
        +
        δ
        E
      
    
    {\displaystyle E+\delta E}
  
. It is mathematically represented as a distribution by a <a href="/facts/Probability_density_function/zvfybna4">probability density function</a>, and it is generally an average over the space and time domains of the various states occupied by the system. The density of states is directly related to the <a href="/facts/Dispersion_relation/oo7RM5eg">dispersion relations</a> of the properties of the system. High DOS at a specific energy level means that many states are available for occupation.
</p><p>Generally, the density of states of matter is continuous. In <a href="/facts/Isolated_system/jheEBts7">isolated systems</a> however, such as atoms or molecules in the gas phase, the density distribution is <a href="/facts/Discrete_distribution/EpsKKVRu">discrete</a>, like a <a href="/facts/Spectral_density/q3Rfs7b0">spectral density</a>. Local variations, most often due to distortions of the original system, are often referred to as local densities of states (LDOSs).
</p>

Density of states open-in-new

Density of states