- #1
Arya_
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Hi All,
My question is more from applied quantum mechanics. Suppose I have a 2D conductor(or semiconductor). I use eigenstate representation of hamiltonian in transverse direction and real space representation in longitudinal direction (direction of current flow). Now,
1. Hω=Eω , ω being eigenstates and E eigenvalues.
2. To find H we need kinetic energy + U (potential).
3. we can find n = electron density by ωω* . density matrix.
4. once n is found we can calculate U (Hartree potential) by Poissons equation.
1 and 4 are solved self consistently until U satisfies both equations.
If I have the H matrix after the self consistent loop is over i.e. I have actual value of potential U. Then what is the physical interpretation for Eigenvalues of H, are they the allowed energy levels??
Thanks in advance,
-Arya
My question is more from applied quantum mechanics. Suppose I have a 2D conductor(or semiconductor). I use eigenstate representation of hamiltonian in transverse direction and real space representation in longitudinal direction (direction of current flow). Now,
1. Hω=Eω , ω being eigenstates and E eigenvalues.
2. To find H we need kinetic energy + U (potential).
3. we can find n = electron density by ωω* . density matrix.
4. once n is found we can calculate U (Hartree potential) by Poissons equation.
1 and 4 are solved self consistently until U satisfies both equations.
If I have the H matrix after the self consistent loop is over i.e. I have actual value of potential U. Then what is the physical interpretation for Eigenvalues of H, are they the allowed energy levels??
Thanks in advance,
-Arya