feat(QuantumMechanics): LinearPMap state observables#1094
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jstoobysmith merged 22 commits intoMay 19, 2026
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This file/PR defines the expectation value, centered vector, variance, and standard deviation of `T` in the state `ψ`, for a partial linear map `T` on a complex inner product space and a vector `ψ ∈ T.domain`, building on Unbounded_v2 proposal. This is PR 1 of 3 and adapts a small portion of a larger state-observable and canonical-CCR development (being carried-out at Axiomatic-AI) into physlib. Subsequent PRs will specialize this API to the position and momentum partial maps, and port the CCR uncertainty and equality-condition lemmas. Depends on leanprover-community#1090
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Nice! Will likely have to wait for #1090 to be cleaned up and merged before this. |
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blocked-by-PR |
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Actually the changes of this PR seem logically independent from the changes in #1090. Could separate them out and make this PR now |
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(Sorry maybe not, missed some props used) |
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#1090 is merged and this is unblocked after resolving merge conflicts |
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Opps sorry, some of my comments on #1095 where meant for here. |
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address review's suggestions and update changes from leanprover-community#1094
Consolidated on expectedValue, variance (‖centered‖²), and standardDeviation. The second-order formula is now a lemma, variance_eq_re_inner_sub_expectedValue_sq under the usual hypotheses, not a second definition.
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updated after latest changes to leanprover-community#1094
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Approved - many thanks for iterating with me. Will merge when it finishes the linters (assuming it passes).
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Thank you for the patient review! |
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This is PR 1 of 3 and it adapts a small portion of a larger state-observable and canonical-CCR development from Axiomatic-AI developments into physlib.
This file/PR defines the expectation value, centered vector, variance, and standard deviation of
Tin the stateψ, for a partial linear mapTon a complex inner product space and a vectorψ ∈ T.domain, building on Unbounded_v2 proposal in #1090.Subsequent PRs will specialize this API to the position and momentum partial maps, and port the abstract CCR uncertainty and equality-condition lemmas.