Source-pinned research
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Clear filtersCondensedMatter.TightBindingChain.hamiltonian_energyEigenstate
Plain-language statement
The energy eigenstates satisfy the time-independent Schrodinger equation.
Source project: Physlib
Person-level attribution pending.
CondensedMatter.TightBindingChain.hamiltonian_hermitian
Plain-language statement
The hamiltonian of the tight binding chain is hermitian.
Source project: Physlib
Person-level attribution pending.
CondensedMatter.TightBindingChain.quantaWaveNumber_exp_N
Project documentation
The quantized wavenumbers form a subset of the BrillouinZone. -/ lemma quantaWaveNumber_subset_brillouinZone : T.QuantaWaveNumber ⊆ T.BrillouinZone := by rintro _ ⟨n, rfl⟩ have hT := T.a_pos have hNpos : 0 < T.N := lt_of_le_of_lt (Nat.zero_le _) n.isLt simp only [BrillouinZone, Set.mem_Ico] generalize T.N = x at * generalize T.a = a at * have hx : (0 :...
Source project: Physlib
Person-level attribution pending.
CondensedMatter.TightBindingChain.quantaWaveNumber_subset_brillouinZone
Plain-language statement
The quantized wavenumbers form a subset of the BrillouinZone.
Source project: Physlib
Person-level attribution pending.
ConjTensorSpecies.conjT_conjT
Plain-language statement
Conjugation is an involution: conjugating twice returns the original tensor, up to the bar_involution recolouring (the identity permutation permT).
Source project: Physlib
Person-level attribution pending.
ConjTensorSpecies.conjT_contrT
Plain-language statement
Conjugation commutes with contraction: conjugating a contracted tensor equals contracting the conjugate on the bar-images of the same two slots.
Source project: Physlib
Person-level attribution pending.