GQM:020117Hahn echo FPF=P returns |+x> with Mx=1 for every static delta; Gaussian ensemble without pulse is exp(-1/2) at sigma tau=1/2Graduate Quantum Mechanics 2 Hahn Echo Static RefocusGraduate Quantum Mechanics 2 Gaussian Detuning EnsemblePrivateLabels unavailablePrivate saving unavailableTime-dependent dynamics, Floquet theory, and geometric phaseGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020218Gaussian eikonal through eta^2 at k=a=1, eta=1/2, q=0 equals -1/4+i/32Graduate Quantum Mechanics 2 Gaussian Eikonal ExpansionGraduate Quantum Mechanics 2 Eikonal Second Order SamplePrivateLabels unavailablePrivate saving unavailableS matrices, resonances, and many-channel scatteringGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020319Single-pair BCS at xi=3/4, Delta=1 has E=5/4, ground=-1/2, u^2=4/5, v^2=1/5, uv=2/5Graduate Quantum Mechanics 2 Single Pair Bcs Even SectorGraduate Quantum Mechanics 2 Bogoliubov Coherence FactorsPrivateLabels unavailablePrivate saving unavailableIdentical particles, Fock space, and second quantizationGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020320Two-mode fermionic Gaussian C=[[3/4,1/4],[1/4,1/2]] has Wick <n1 n2>=5/16, Cov=-1/16, Var(N)=5/16Graduate Quantum Mechanics 2 Fermionic Correlation SpectrumGraduate Quantum Mechanics 2 Gaussian Wick Number LedgerPrivateLabels unavailablePrivate saving unavailableIdentical particles, Fock space, and second quantizationGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020322Jordan-Wigner strings give adjacent σ_j^- σ_{j+1}^+=c_j^dag c_{j+1} and σ_1^- σ_3^+=c_1^dag(1-2n_2)c_3, so physical <100|O|001>=<110|O|011>=+1 while bare c_1^dag c_3 gives +1 then -1Graduate Quantum Mechanics 2 Jordan Wigner Car ParityGraduate Quantum Mechanics 2 Three Site String Matrix ElementsPrivateLabels unavailablePrivate saving unavailableIdentical particles, Fock space, and second quantizationGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020421Euclidean free kernel at m=hbar=1, tau=2, xi=0, xf=1 is e^{-1/4}/(2 sqrt(pi)) with variance 2Graduate Quantum Mechanics 2 Euclidean Heat Kernel SemigroupGraduate Quantum Mechanics 2 Free Particle Euclidean SamplePrivateLabels unavailablePrivate saving unavailablePath integrals and semiclassical expansionGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020423The cubic bounce of V=½mω²x²-gx³/3 has xb=mω²/g, xt=3mω²/(2g), xB=xt sech²[ω(τ-τ0)/2], and SB=6m³ω⁵/(5g²); at m=ω=hbar=1, g=1/2 one has xb=2, xt=3, ΔV=2/3, SB=24/5Graduate Quantum Mechanics 2 Cubic Bounce ProfileGraduate Quantum Mechanics 2 Cubic Bounce ActionPrivateLabels unavailablePrivate saving unavailablePath integrals and semiclassical expansionGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020424Two Euclidean delta sources at separation ln 2 give G(0)=1/2, G(ln 2)=1/4, JGJ=3/2, Z[J]/Z0=e^{3/4}, means 3/4 at both sources, connected cross 1/4, and full cross 13/16Graduate Quantum Mechanics 2 Euclidean Source Generating FunctionalGraduate Quantum Mechanics 2 Two Delta Source CorrelatorsPrivateLabels unavailablePrivate saving unavailablePath integrals and semiclassical expansionGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020525The Klein-Gordon Noether current of φ=(1/2)e^{-ip·x} at p=(5,3,0,0), m=4 is j=(5/2,3/2,0,0) with j²=4; the conjugate mode flips the sign and a real field has j=0Graduate Quantum Mechanics 2 Klein Gordon Noether ConservationGraduate Quantum Mechanics 2 Klein Gordon Plane Wave CurrentPrivateLabels unavailablePrivate saving unavailableKlein-Gordon and Dirac equationsGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020526The supercritical KG step m=12, E=13, qV=33 has kL=5, pR=-16, r=-21/11, t=-10/11 and charge-current ratios R=441/121, T=-320/121 with R+T=1Graduate Quantum Mechanics 2 Klein Gordon Supercritical MatchingGraduate Quantum Mechanics 2 Klein Zone Charge CurrentPrivateLabels unavailablePrivate saving unavailableKlein-Gordon and Dirac equationsGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020627Natural-log D(|0><0||(I+(3/5)X)/2)=ln(5/2); Z-dephasing drops it by ln(5/4), the reverse is infinite, and Pinsker holds at 17/25View access optionsGraduate Quantum Mechanics 2 Quantum Relative Entropy SupportGraduate Quantum Mechanics 2 Dephasing Dpi PinskerPrivateLabels unavailablePrivate saving unavailableDensity operators, open systems, entanglement, and channelsGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020628Product |+>^4 has QFI 4 under G=(1/2)sum Z_j while GHZ4 has QFI 16, and the GHZ-parity measurement saturates the boundView access optionsGraduate Quantum Mechanics 2 Pure State Qfi Generator VarianceGraduate Quantum Mechanics 2 Ghz Parity Classical FisherPrivateLabels unavailablePrivate saving unavailableDensity operators, open systems, entanglement, and channelsGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020629Haar average purity of a 2x2 bipartite reduction is 4/5 by the swap trick, with E|r|^2=3/5 and E det rho_A=1/10View access optionsGraduate Quantum Mechanics 2 Haar Symmetric Subspace AverageGraduate Quantum Mechanics 2 Swap Trick Reduced PurityPrivateLabels unavailablePrivate saving unavailableDensity operators, open systems, entanglement, and channelsGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020630The Peres-Mermin square has row products +I,+I,+I and column products +I,+I,-I, so no noncontextual +-1 assignment existsView access optionsGraduate Quantum Mechanics 2 Peres Mermin Context ProductsGraduate Quantum Mechanics 2 Noncontextual Assignment ObstructionPrivateLabels unavailablePrivate saving unavailableDensity operators, open systems, entanglement, and channelsGraduate Quantum Mechanics II · Mixed reviewProgress not loaded
GQM:020631Independent bit-flip p=0.1 on the three-qubit code has logical error 0.028 after syndrome recovery, strictly below p for 0<p<1/2View access optionsGraduate Quantum Mechanics 2 Bit Flip Stabilizer SyndromeGraduate Quantum Mechanics 2 Independent X Logical ErrorPrivateLabels unavailablePrivate saving unavailableDensity operators, open systems, entanglement, and channelsGraduate Quantum Mechanics II · Mixed reviewProgress not loaded