Commutation Angle

The coefficient ci has a maximum value of 2 when a is zero and the commutation angle u is assumed to be negligibly small. 

Figure 15.4 Trapezoidal current in the supply side of a six-pulse thyristor bridge, with the commutation angle u = 20°.

The average value of the waveform is zero because it is symmetrical about the Y-axis, and so the coefficient for the average value is zero. The sinusoidal function in the coefficient a varies with the commutation angle u and approaches a limiting value when u is small,... 

The effect of the commutation angle u on the 180°, 60° and supply current waveforms is the same as found in sub-section 15.3.2 for the 120° waveform. Therefore each coefficient becomes,... 

Assume the inverter output line current consists of a 120° rectangle wave and that the commutation angle u is small enough to be ignored. The complete waveform has a harmonic content of,... 

As a result, the eigenfunctions of Hj-ot are those of J2 (and Ja as well as Jz both of which commute with J2 and with one another Jz is the component of J along the lab-fixed Z-axis and commutes with Ja because Jz = - ih 3/3(1) and Ja = - ih 3/3% act on different angles). The energies associated with such eigenfunctions are... 

Z-axis and commutes with Ja because Jz = - ih 3/3(1) and Ja = - ih 3/3% act on different angles). The energies associated with such eigenfunctions are... 

If the time-dependent Hamiltonian under MAS commutes with itself at all points in time, i. e., TLih) = 0 for all values of and t2, magic-angle spinning will lead to... 

The px, Py and pz orbitals are eigenfunctions of the if angular momentum operator with eigenvalues equal to L(L+1 )4f = 2 hf. Since if andLz commute and act on the same (angle) coordinates, they possess a complete set of simultaneous eigenfunctions. 

Exercise 12.5-4 Show that two rotations through infinitesimally small angles commute. 

An applied field in the xy-plane can tune the tunnel splittings Amm. via the Sx and Sy spin operators of the Zeeman terms that do not commute with the spin Hamiltonian. This effect can be demonstrated by using the Landau-Zener method (Section 3.1). Fig. 8 presents a detailed study of the tunnel splitting A 10 at the tunnel transition between m - +10, as a function of transverse fields applied at different angles (p, defined as the azimuth angle between the anisotropy hard axis and the transverse field (Fig. 4). 

Here, we call the attention of the reader that our Eq. (24) in the previous interlude correspond to Eqs. (32) in Ref. [3] for the cartesian components of the angular momentum in the body frame and the inertial frame, respectively, in terms of the Euler angles. Notice that the angles if and

commutation rules from Eq. (22) in Ref. [3], for the analysis of the rotations of asymmetric molecules are as follows ... 

---