Does tunneling transmission probability depend on the density of states or velocity?

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1. Sep 28, 2014

asheg

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. (T(E)=C×DOS1(E)×DOS2(E), where C is constant). However, in Landauer transmission formula (without tunneling) the transmission depends on both DOS and velocity of carriers (T(E)=C′×DOS(E)×v). So I am wondering if velocity is important too? If yes, which velocity in which region?!

[1] For example, see "Introduction to Many-body quantum theory in condensed matter physics", Bruus et al.

2. Sep 29, 2014

ZapperZ

Staff Emeritus
The velocity comes in in the form of the kinetic energy of the tunneling particle. So it is explicitly a factor in any tunneling probability for a finite potential.

Zz.