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{{no footnotes|date=May 2012}}
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In [[NMR spectroscopy]], the '''product operator formalism''' is a method used to determine the outcome of [[pulse sequence]]s in a rigorous but straightforward way. With this method it is possible to predict how the bulk [[magnetization]] evolves with time under the action of pulses applied in different directions. It is a net improvement from the semi-classical vector model which is not able to predict many of the results in NMR spectroscopy and is a simplification of the complete density matrix formalism.


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In this model, for a single [[spin (physics)|spin]], four base operators exist: <math>I_x</math>, <math>I_y</math>, <math>I_z</math> and <math>E/2</math> which represent respectively polarization (population difference between the two spin states), single quantum coherence (magnetization on the xy plane) and the unit operator. Many other, non-classical operators exist for [[Quantum coupling|coupled systems]]. Using this approach, the evolution of the magnetization under free precession is represented by <math>I_z</math> and corresponds to a rotation about the z-axis with a [[phase angle]] proportional to the [[chemical shift]] of the spin in question:


JT Foxx asks Nido, �What are your opinions on starting up a protection finance?� Nido responses to him, �Commencing that is simple; it is dealing with it that is not straightforward. You possibly need to find another person in this business and partner with them. The purpose is to gain income and invest in so people investing in the budget get a  [http://tinyurl.com/pch83be http://tinyurl.com/pch83be] revenue. Government ordinances are very cumbersome that you should really think through that extensiv<br>y.�
<math>I_x \xrightarrow{\omega \tau I_z} \cos (\omega \tau)I_x - \sin (\omega \tau)I_y </math>


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Pulses about the x and y axis can be represented by <math>I_x</math> and <math>I_y</math> respectively; these allow to interconvert the magnetization between planes and ultimately to observe it at the end of a sequence. Since every spin will evolve differently depending on its shift, with this formalism it is possible to calculate exactly where the magnetization will end up and hence devise pulse sequences to measure the desired signal while excluding others.


What's the associated risk? The dumbest element would be to place it all in a perception. The ideal thing to undertake is to declare I have $10 under my name, put a part of that aside for security and safety so that you feel protected, in order that you can think you could be inventive; what is the sum you require in order to feel secure and protected. Then how about what's left could you risk? Let me research correctly and diligently so that I am not a risk taker but a risk manager. How can I perform this thing that is not guaranteed and take care of it. How can I not land up losing? Taking a day off once a week to concentrate on Promotion and become strategic. That is a smart idea if it works<br><br> you.  
The product operator formalism is particularly useful in describing [[Two-dimensional nuclear magnetic resonance spectroscopy|experiments in two-dimensions]] like COSY, HSQC and HMBC.  


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== References ==
*{{cite web | publisher = [[University of California, Irvine]] | title = Understanding NMR Spectroscopy | author = James Keeler | format = reprinted at [[University of Cambridge]] | url = http://www-keeler.ch.cam.ac.uk/lectures/Irvine/ | accessdate = 2012-08-05}}
*{{cite web|publisher=[[University of Texas]]|title=A Pictorial Representation of Product Operator Formalism|author=David Donne|coauthor=David Gorenstein|url=http://www.biophysics.org/Portals/1/PDFs/Education/donne.pdf|accessdate=2012-08-05}}


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[[Category:Nuclear magnetic resonance]]
 
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Nido tells JT Foxx, �How do you get unstuck in your firm? Typically, once people are �stuck� or stressed, a revival of objective is what works. The personal goal is taking a pad and stating what you are glad for, what you achieved, and you examine it. What do you want to change and realign? You must be in groups that nourish you. How can you connect the most with prosperous people: this is to be in scenarios in which you could do that anyway. I don�t prejudge people but I get the details before I come to a decision; to communicate with individuals the secret is to be in the correct places. Always be on the lookout and in the zone for establishing partnerships and create different business. If you are not at ease with advertising, compose a list of things to get yourself in work mode to be much better.�

Revision as of 21:26, 18 December 2013

Template:No footnotes In NMR spectroscopy, the product operator formalism is a method used to determine the outcome of pulse sequences in a rigorous but straightforward way. With this method it is possible to predict how the bulk magnetization evolves with time under the action of pulses applied in different directions. It is a net improvement from the semi-classical vector model which is not able to predict many of the results in NMR spectroscopy and is a simplification of the complete density matrix formalism.

In this model, for a single spin, four base operators exist: , , and which represent respectively polarization (population difference between the two spin states), single quantum coherence (magnetization on the xy plane) and the unit operator. Many other, non-classical operators exist for coupled systems. Using this approach, the evolution of the magnetization under free precession is represented by and corresponds to a rotation about the z-axis with a phase angle proportional to the chemical shift of the spin in question:

Pulses about the x and y axis can be represented by and respectively; these allow to interconvert the magnetization between planes and ultimately to observe it at the end of a sequence. Since every spin will evolve differently depending on its shift, with this formalism it is possible to calculate exactly where the magnetization will end up and hence devise pulse sequences to measure the desired signal while excluding others.

The product operator formalism is particularly useful in describing experiments in two-dimensions like COSY, HSQC and HMBC.

References