יחס נפיצה – הבדלי גרסאות

ב[[פיזיקה]], '''יחס נפיצה''' הוא הקשר (המתמטי) בין ה[[אנרגיה]] E של המערכת ל[[תנע]] <math>\vec{p}</math> שלה; או לחילופין הקשר בין ה[[תדירות]] של [[גל]] <math>\omega</math> לוקטור הגל <math>\vec{k}</math>. ב[[מכניקת הקוונטים]] ו[[מכניקה סטטיסטית]] מדברים גם על יחס נפיצה בין האנרגיה לוקטור הגל.

 

 

עבור חלקיק חופשי יחס הנפיצה הוא:

למערכות מורכבות יותר יהיה יחס נפיצה מורכב יותר או שונה.

 

 

:<math> \omega = c | \vec{k} | = ck </math>

כאשר הסתמכנו על יחס הנפיצה היחסותי ל[[פוטון]], חלקיק חסר מסה, <math>\ E = c p</math>.

:<math> v = \frac{\partial E}{\partial p} = \frac{\partial \omega}{\partial k} = c.</math>

וזוהי [[מהירות האור]].

 

The name "dispersion relation" originally comes from [[optics]]. It is possible to make the effective speed of light dependent on wavelength by making light pass through a material which has a non-constant [[index of refraction]], or by using light in a non-uniform medium such as a [[waveguide]]. In this case, the waveform will spread over time, such that a narrow pulse will become an extended pulse, i.e. be dispersed. In these materials, <math>\frac{\partial \omega}{\partial k}</math> is known as the [[group velocity]] and correspond to the speed at which the peak propagates, a value different from the [[phase velocity]].

 

 

In the study of solids, the study of the dispersion relation of electrons is of paramount importance. The periodicity of crystals mean that for a given momentum, many levels of energy are possible, and that some energies might not be available at any momentum. The collection of all possible energies and momenta is known as the [[band structure]] of a material. Properties of the band structure define whether the material is an [[Electrical insulation|insulator]], [[semiconductor]] or [[Conductor (material)|conductor]].

 

 

The dispersion relation of [[phonon]]s is also important and non-trivial. Most systems will show two separate bands on which phonons live. Phonons on the band that cross the origin are known as [[acoustic phonon]]s, the others as [[optical phonon]]s.

* [[גל]]

 

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