Density_Matrix_10

# Density_Matrix_10 - Density Matrix Description of NMR...

This preview shows pages 1–6. Sign up to view the full content.

Density Matrix Description of NMR BCMB/CHEM 8190

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Some Sequences Need Quantum Explanations For example: the INEPT and HSQC Experiments Solution: density matrix and product operator descriptions 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->
Operators in Matrix Notation If we stay with one basis set, properties vary only because of changes in the coefficients weighting each basis set function μ x = γ (h/2 π )< ψ | Ix | ψ > ψ = c1 αα + c2 αβ + c3 βα + c4 ββ = j c j φ j < ψ | Ix | ψ > = j,k c j * c k < φ j | Ix | φ k > We need calculate < φ j | Ix | φ k > only once if we stay with this basis set – these can be put in a n x n matrix. Matrix equivalent: < ψ | Ix | ψ > = (c1, c2, …)* Ρਟ Τ੏ Λি c1 Ξ৯ Ο৿ Ix Ο৿ Ο৿ c2 Ο৿ Σਿ Φ੯ Νয় Πਏ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Special Case: Pauli Spin Matrices 0 ½ ½ 0 |Ix| = Note: < α | Ix | α > = ½ < α | β > = 0 < α | Ix | β > = ½ < α | α > = ½ 0 -i ½ i ½ 0 |Iy| = ½ 0 0 ½ |Iz| = How do they work? Try something we know: Ix | α > = ½ β 0 ½ ½ 0 1 0 0 ½ 0 1 = = ½ = ½ β Operators are a matrix of numbers, Spin functions a vector of numbers
Density Matrices and Observables for an Ensemble of Spins Expectation values pertain to single spin properties; we observe net behavior of an ensemble of spins. For a particular system (two spin ½ nuclei) operator representations are the same; all variations are in basis set coefficients. We need to average over these coefficients.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern