k.p Perturbation Theory L1-326

Quantum MechanicsNear-gap band structure expansionδ=3 · standardL_DAG = 3.1📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

E_{n} (k) = E_{n} (k_{0}) + hba r^{2} k^{2} / (2 m_{e}) + m! = n \sum ∣ < u_{n} ∣ p ∣ u_{m} > ∣^{2} \cdot (hba r \cdot k)^{2} / (m_{e}^{2} \cdot (E_{n} - E_{m}))

k.p: expand H(k) around high-symmetry point k_0 using momentum matrix elements p_{nm}; effective mass and g-factor from band curvature.

L-DAG

E.momentum_matrix -> E.perturbative_expansion -> O.effective_mass

E.momentum_matrixE.perturbative_expansionO.effective_mass

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 200

Well-posed near k_0; fails far from band edge.

Solvability C

Solver class:: Kane 8-band, Luttinger 6-band models; fits Luttinger gamma from cyclotron
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.