The thermal wavelength of Broglie is a concept of the Physique statistics and quantum Mécanique. It is a statistical size and it represents the wavelength of Broglie average of a particle to some Température. This thermal wavelength characterizes spreading out space of the associated particle and the bond between traditional mechanics and quantum.

Definition

Mass particles

According to the principle of the Duality wave-corpuscle, a particle can have a Wavelength of $\backslash \; lambda=h/p$. For a Perfect gas, the energy of a particle is $k\_B\; T$. One can then define the thermal wavelength of Broglie $\backslash \; lambda\_\; \{HT\}$ of a mass particle in balance of a perfect gas like:

$\backslash \; lambda\_\; \{HT\}\; =\; \backslash \; frac\; \{H\}\; \{\backslash \; sqrt\; \{2\; \backslash \; pi\; mk\_\; \backslash \; mathrm\; \{B\}\; T\}\}\; =\; \backslash \; frac\; \{2\; \backslash \; pi\; \backslash \; hbar\}\; \{\backslash \; sqrt\; \{2\; \backslash \; pi\; mk\_\; \backslash \; mathrm\; \{B\}\; T\}\}$.

• H is the Constante of Planck
• m is the Masse of a gas particle
• K is the Boltzmann constant
• T is the Temperature gas.

Particles without mass

Physical direction

The thermal length of Broglie represents a means to determine if the system must be considered in a quantum or traditional way. Indeed, the effects quantum start starts to be important when the thermal wavelength of Broglie becomes comparable with the other lengths characteristic of the system, like the Libre range of a particle, or the volume of the system. In the framework of the Supraconductivity, the Transition from phase between a traditional system and a quantum system, is carried out at a certain temperature, that one names Température criticizes. In lower part of this temperature, in fact the quantum effects dominate over the system.

See too

• Wavelength
• wavelength of Broglie