Tunneling Transmission Probability: DOS or Velocity?

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SUMMARY

The discussion centers on the relationship between tunneling transmission probability and the density of states (DOS) and velocity of carriers in quantum mechanics. The tunneling transmission formula is defined as T(E)=C×DOS1(E)×DOS2(E), while the Landauer transmission formula incorporates both DOS and carrier velocity, expressed as T(E)=C′×DOS(E)×v. The inquiry raised is whether velocity plays a significant role in tunneling probability and, if so, which specific velocity should be considered in each region involved in the tunneling process.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the concept of density of states (DOS)
  • Knowledge of the Landauer transmission formula
  • Basic grasp of kinetic energy in quantum particles
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  • Research the implications of velocity in quantum tunneling scenarios
  • Study the differences between tunneling and Landauer transmission formulas
  • Explore the role of kinetic energy in tunneling probabilities
  • Investigate advanced quantum mechanics textbooks for deeper insights
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Quantum physicists, researchers in condensed matter physics, and students studying quantum mechanics who seek to understand the factors influencing tunneling transmission probabilities.

asheg
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In some quantum textbooks [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.
 
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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.
 

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