Calculating Mean Thermal Wavelength for Relativistic Particles | Tutorial"

[shahrzad64]

hi
i want to calculate "mean thermal wavelenght for relativistic particles"for example for photon .
i don't khow how can i do it.
please help me.
thankyou.

 

[Gokul43201]

There are different (final) equations for massless particles than for massive particles. For massless particles, you use,
$$\lambda = \frac{hc}{\pi^{1/3} 2kT}$$
and for massive particles, you use the thermal de Broglie wavelength. In general, you can extract a thermal wavelength out of the dispersion relation for the particle.

 

[shahrzad64]

There are different (final) equations for massless particles than for massive particles. For massless particles, you use,
$$\lambda = \frac{hc}{\pi^{1/3} 2kT}$$
and for massive particles, you use the thermal de Broglie wavelength. In general, you can extract a thermal wavelength out of the dispersion relation for the particle.

thankyou for your answer
i know this relation for phonon,but can you send for me relations ,that give this equetion .
in fact ,i don't khow how can i obtain this equation
thankyou

 

[Gokul43201]

One answer is that it is simply defined this way, and needs no derivation, but that would not be an accurate statement. In fact, there is a paper that proposes a generalized equation for the thermal wavelength for all particles (living in n-dimensional space) with a power law dispersion relation.

Z. Yan, "General thermal wavelength and its applications", Eur. J. Phys. 21 (2000) 625