Effective mass is defined by analogy with Newton's second law F=m a. Using quantum mechanics it can be shown that for an electron in an external electric field E:
where a is acceleration, h is Planck's constant, k is the wave number[?] (often loosely called momentum since k = p / h), ε(k) is the energy as a function of k, or the dispersion relation[?] as it is often called. From the external electric field alone, the electron would experience a force of qE, where q is the charge. Hence under the model that only the external electric field acts, effective mass m^{*} becomes:
For a free particle, the dispersion relation is a quadratic, and so the effective mass would be constant (and equal to the real mass). In a crystal, the situation is far more complex. The dispersion relation is not even approximately quadratic, in the large scale. However, wherever a minimum occurs in the dispersion relation, the minimum can be approximated by a quadratic curve in the small region around that minimum. Hence, for electrons which have energy close to a minimum, effective mass is a useful concept.
In energy regions far away from a minimum, effective mass can be negative or even approach infinity. Effective mass is generally dependent on direction (with respect to the crystal axes[?]), however for most calculations the various directions can be averaged out.
Effective mass should not be confused with reduced mass, which is a concept from Newtonian mechanics. Effective mass can only be understood with quantum mechanics.
Material  Electron effective mass  Hole effective mass 

Silicon  1.91 m_{e}  1.00 m_{e} 
Gallium arsenide  0.067 m_{e}  0.45 m_{e} 
Germanium  0.55 m_{e}  0.37 m_{e} 
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