Tight Binding Hamiltonian and Potential (U)

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SUMMARY

The discussion centers on the application of potential values (U) in the context of a tight binding Hamiltonian for a 3D solid. It is established that one can directly incorporate the potential profile values (V(x)) into the tight binding Hamiltonian without the need for transformation, as the potential function adheres to the superposition principle. The tight binding Hamiltonian is described as an empirical effective Hamiltonian, parameterized to yield accurate energies for the lowest eigenstates, while also accounting for contributions from excited atomic states.

PREREQUISITES
  • Understanding of tight binding Hamiltonians
  • Familiarity with potential energy profiles in solid-state physics
  • Knowledge of eigenstates and their significance in quantum mechanics
  • Concept of superposition principle in quantum systems
NEXT STEPS
  • Research the derivation of the tight binding Hamiltonian in solid-state physics
  • Explore the implications of potential energy profiles on electronic band structure
  • Study the superposition principle and its applications in quantum mechanics
  • Investigate the role of excited atomic states in Hamiltonian formulations
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Physicists, materials scientists, and students studying quantum mechanics and solid-state physics, particularly those interested in the modeling of electronic properties in materials using tight binding approximations.

Arya_
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Hi All,

Greetings !

Here is what I wish to know. Specifying a tight binding hamiltonian requires values of potential (U). Consider a 3d solid. If I have potential profile in x direction (U1, U2, U3...so on) can I directly plug in these U values into the tight binding hamiltonian or do I need to do some transformation (like change of space etc) before I can plug in 'potential values vs X' into Hamiltonian.

Thanks,
-Arya
 
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Yes,I think you can directly plug in these V(x) values into the tight binding hamiltonian.Because potential function meets the superposition principle.
 
The tight binding hamiltonian is an empirical effective hamiltonian which is parametrized in such a way as to give correct energies for the lowest eigenstates of the hamiltonian. Excited atomic states also make a contribution, also to the potential. So there is no 1 to 1 correspondence between some potential in the full hamiltonian and the U's appearing in the tight binding approximation.
 

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