feat(PhyslibAlpha): maximal current state of the open tight binding chain - #1716
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…hain Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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jstoobysmith
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Approved - will merge shortly.
77b61f4
hello guys joseph, timeroot, here again with a short one. what this PR exactly does?
it adds "TightBindingChain/MaxCurrentState.lean" (300 lines), it comes directly from #1708 (current eigenstates) and #1709 (uncertainty on T.HilbertSpace). the longest standing wave, k = 1, is the one with the biggest current, so here we normalize it and compute its expectations. only 4 notes:
1.- "currentEigenvalue_le_one": for t ≥ 0, k = 1 carries the largest current 2 a t cos(pi/(N+1)) among all the current eigenstates.
2.- "maxCurrentState", "norm_maxCurrentState": the k = 1 eigenstate normalized, norm exactly 1.
3.- "expectation_openHamiltonian_maxCurrentState", "expectation_position_maxCurrentState": (H) = E0, the centre of the band, and (X) = a (N-1)/2, the centre of the chain.
4.- "expectation_bracket_maxCurrentState", "robertson_schrodinger_maxCurrentState": ((H, X)) = -a t cos(pi/(N+1)) and the energy-position uncertainty relation on this state.
why? this is the state where the next PR (#1718) checks when the uncertainty relation becomes an equality.
tks a lot guys, im here waiting for the review and ready for any changes¡