Quantum_intro_10

Quantum_intro_10 - BCMB/CHEM 8190 Spin Operators and QM...

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BCMB/CHEM 8190 Spin Operators and QM Applications
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Quantum Description of NMR Experiments • Not all experiments can be described by Bloch equations – scalar coupling examples • Hamiltonians and Schrodinger’s equation • Density matrix and Lioville-VonNeuman eq • Product operators and transformation rules • INEPT and HSQC examples
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Some Pulse Sequences Have Classical (Bloch) Explanations Spin-Echo Experiment – J Coupling Effects 180° pulse refocus chemical shifts, inhomogenieties, not Js x y z ω –J/2 ω +J/2 x y z x y z This can be used to measure T 2 relaxation or scalar coupling in a 2D experiment (observe, t 2 ) 90x 180y x y z ω +J/2 ω –J/2 J t 1 t 1 /2 t 1 /2
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Some Sequences Need Quantum Explanations Mixing by Scalar Coupling of Directly Bonded Nuclei: the INEPT and HSQC Experiments 15 N 1 H 1 H 15 N 90x 180y 90y 90x x y z x y z x y z x y z x y z x y z J-> J->
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Quantum Mechanics Fundamentals (Spin Operations) Expectation values correspond to observables: μ = < ψ | μ | ψ > = ⌠ψ * μ ψ d τ μ - an operator, ψ - a wave function (spin function) Examples: ψ
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Quantum_intro_10 - BCMB/CHEM 8190 Spin Operators and QM...

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