R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....The sample, which is placed in a strong unidirectional magnetic eld, is subjected to a temporal sequence of radio frequency pulses, and each molecule functions as an autonomous computational unit. The result of the computation, which is read o by means of the usual techniques of NMR spectroscopy [39], is the ensemble average of the computer outputs taken with respect to the state of all the molecules in the sample. Because NMR experiments are conducted at room temperature ( 300 K) the initial state of the sample is the thermal equilibrium state exp ( H) Z , where H is the Hamiltonian of ....

R.R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1994).

....of shift and modulation theorems for the QFT that closely resemble the corresponding theorems of the complex Fourier transform [22] For real 2 D signals, the QFT is identical to the 2 D Clifford Fourier transform. A 2 D hypercomplex transform was first introduced by Ernst et al. 5] [23] without reference to a specific 4 D hypercomplex algebra. Ell [24] 25] introduced the QFT in the form (29) in the context of partial differential systems. Sangwine [26] used the QFT as a Fourier transform for color images. Chernov used the discrete QFT for the development of 2 D FFT algorithms ....

R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions. New York: Oxford, 1985.

....briefly discussed in Appendix A (see [35] was given by Hahn and Torrey (14, 13) One can also obtain a spatial scale # 1 by considering the second term in the exponent of [6] and writing its contribution as a factor exp[ i z #1 t #1 ] where the length scale # 1 is # 1 = 3 # D 3#G . [25] 22 A second avenue to obtain parameters which allow one to estimate the e#ect of di#usion on MRI images involves the following qualitative considerations. Di#usion implies that over a time scale # 2 , position di#erences develop on a length scale # 2 determined by # 2 2 # D# 2 [26] At the ....

....2 or # 2 . Using [26] and eliminating # 2 in [27] yields # 1 2 # 3 # D# 2 G 2 # 2 , 28] an expression which reproduces the Hahn and Torrey (14, 13) result [24] except for a factor of about 0.6. Using [26] to eliminate instead # 2 yields 4 # 2 # 3 # #D #G [29] which reproduces [25] except for a factor of about 2. 4 For heuristic reasons, we have kept an extra factor of # in expression [29] while disregarding all other numerical factors: the resulting parameter q assumes the numerical value q =1forvaluesof G and D at which edge intensity peaks just begin to merge to a ....

R. R. Ernst, G. Bodenhausen, and A. Wokaun: "Principles of Nuclear Magnetic Resonance in One and Two Dimensions". Clarendon Press, Oxford, 1987.

....P j k ( 1 = E j P j P j 1 t 2ph E 0 m = i h H rest t exp 1 = i h H interaction t exp 1 = G E S 0 = 133 this case the terms in (5.92) cancel each other. The corresponding notion is the resonant pulse for nuclear spin quantum computing [91]. The pulse has an effect only if its frequency equals the resonance frequency. In practice, the third coordinate of is not zero, but it must be much smaller than the first: For a multi qubit operation gE 0 . Combining the two inequalities and dividing by E 0 leads to . Thus for the error of ....

R. R. Ernst, G. Bodenhausen and A. Wokaun, Principles of Nuclear Magnetic resonance in One and Two Dimension (Clarendon Press, Oxford, 1987). 190

....that most familiar to the muon community. All that is written here can be found in many standard textbooks. They will not be quoted extensively; it suffices perhaps to do it now by saying that some texts [1, 2] are basic and thorough, some[3] are very introductory and hardware oriented, while some [4, 5] are more advanced. The other lectures select two topics where NMR and SR have both contributed. The second lecture is focused on relaxation in metals and superconductors, with one example of historic relevance and some more recent ones. The third and last lecture takes critical fluctuations in ....

....species. In this case the Zeeman levels of each spin are more than two and it is convenient to write the M ff in terms of the level populations. Equation 7 then becomes a matrix equation with as many solutions as the allowed transitions, hence the relaxation is a linear combination of exponentials[5, 6]. Coming back to the simple I = 1=2 case we must work out the left hand side of equation 8. We already know what spin dynamics to expect: it will be a damped precession and we can get rid of the trivial harmonic motion by moving to the RRF. In quantum mechanics the equivalent of this is (broadly ....

Ernst R E et al. 1987 Principles of Nuclear Magnetic Resonance in One and Two Dimensions Clarendon Press, Oxford.

.... physics [29] Nuclear magnetic resonance also provides an experimental paradigm for the study of multiparticle geometric algebra, as elegantly developed in [20, 21, 48] The reason is that the so called product operator formalism, on which the modern theory of NMR spectroscopy is largely based [7, 8, 16, 24, 46, 47, 51, 57], is a nonrelativistic quotient of the multiparticle Dirac (i.e. space time [33] algebra. Thus NMR provides a natural and surprisingly easy way to experimentally verify some of the predictions of multiparticle quantum mechanics, as derived by geometric algebra. The existence of a concrete ....

....k 1 # k 2 # k 2 # k 3 # k 3 (# k # k # # 0. # k . 0 ) precesses about the applied magnetic field at a constant rate # k 0 . This so called Bloch vector describes the observable macroscopic magnetization due to polarization of the k th spin over all molecules of the ensemble [24, 26]. In NMR spectroscopy, the spins are controlled by pulses of RF (radiofrequency) radiation about the z axis. The corresponding Hamiltonian H RF = 1 2 #N k=1 # k 1 # cos(#t)# k 1 sin(#t)# k 2 # (1.24) is time dependent, which normally makes it impossible to give a closedform ....

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R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford Univ. Press, U.K., 1987.

.... of such spins in the sample[5] It is also customary in NMR spectroscopy to shift the reduced density matrix by subtraction of 2 Gamman times the trace of the equilibrium reduced density matrix, since only the traceless part undergoes unitary evolution, and to scale it to have integral elements[6]. In the next paragraph, we define a manifold of statistical spin states with a reduced density matrix whose traceless part is proportional to the traceless part of the usual density matrix of a pure state. In the following, whenever we use the term density matrix , we mean reduced, shifted and ....

....operators , i.e. the products of the usual matrices of one spin operators I x , I y and I z (as above) This makes it very easy to describe the unitary transformations effected by applying RF (radio frequency) pulses to the sample. For example, a =2 pulse about the y axis (in the rotating frame[6]) by definition rotates the equilibrium density matrix to D eq [ 2]y I 1 x I 2 x : 2) This rotated magnetization precesses about the applied field and generates an oscillatory magnetic moment in the xy plane, according to the density matrix obtained from the time dependent unitary ....

Ernst, Richard R., Geoffrey Bodenhausen, and Alexander Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford Univ. Press (1987).

.... of 13 C in 1 H detected experiments where p 0 = pn = 0) The coherence orders during the inter pulse delays (evolution periods) may be cast in row vector form: p = p 0 ; p 1 ; pn ) 9] The pulse phases are represented by a column vector OE: OE = OE 1 ; OE 2 ; OE n ) T [10] Using Deltap = Deltap 1 ; Deltap 2 ; Deltap n ) p 1 Gamma p 0 ; p 2 Gamma p 1 ; pn Gamma pn Gamma1 ) 11] the total phase change of the coherence pathway is given according to the first rule simply by (2, 4 ) Gamma X j ( Deltap j :OE j ) Gamma OE r = ....

R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford (1987).

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R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, 1987.

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Ernst, R., Bodenhausen, G., and Wokaun, A. Principles of Nuclear Magnetic Resonance in one and two dimensions. (Oxford University Press, 1990).

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Ernst, R., Bodenhausen, G., and Wokaun, A. Principles of Nuclear Magnetic Resonance in one and two dimensions. (Oxford University Press, 1990).

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R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford, 1987.

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