The relation between Transmission Spectrum and Density of state

[mephisto3142001]

The plot of Transmission Spectrum is always similar to that of Density of state, and I have consulted the derivation of Transmission Spectrum
from papers and textbooks, showing that calculating Density of state is a required step in the beginning. I want to ask the exact meaning of
Transmission Spectrum and how it is correlated to Density of state.

[Anders Blom]

Indeed, often there is a correlation between this and the transmission. There is however a fundamental difference, because the density of states, which is derived from the lesser Green's function, describes how the electrons populate the available states, whereas in order to have a finite transmission you also need to have available receiving states in the right electrode for the states coming from the left electrode.

[mephisto3142001]

I looked up the topic about transmission spectrum somewhere else in the forum and I found a reply "The transmission spectrum is not the probability of an electron going through the device. The transmission spectrum is the sum of probabilities for all the states that exist at the given energy."
I want to confirm whether my concept is correct.
For  transmission spectrum of DTB device, the energy 2.03eV corresponds to transmission coefficient 0.608, does it mean that
the state at 2.03eV has probabilities 0.608 to exist?

[Anders Blom]

No, it means that the collected tunneling probability for the available states at 2.03 eV is 0.608. In the quote, note that it says "the sum of {the tunneling} probabilities for all the states THAT exist at the given energy", not "the sum of probabilities for all the states TO exist at the given energy".