Angular momentum oibital

In quantum mechanics, three quantum numbers are required to describe the distribution of electrons in hydrogen and other atoms. These numbeis arc derived from the mathematical solution of the Schrodinger equation for the hydrogen atom. They are called the principal quantum number, the angular momentum quantum number, and the magnetic quantum number. These quantum numbeis will be used to describe atomic oibitals and to label electrons that reside in them. A fourth quantum number— the spin quantum number—describes the behavior of a specific electron and completes the description of electrons in atoms. 

The primary difficulty arises from the fact that although it is most convenient to carry out the scattering calculation in a coupled basis [section 2] in which the total angular momentum is a good quantum number, the wavefunction of two atoms at infinite separation can best be expressed in an uncoupled basis. To illustrate this point, consider the initial state of the diatomic (atom+laser-excited atom) prior to collision. Prior to the collision the relative oibital angular momentum d is always oriented peipendicular to the collision plane, in other words d is always perpendicular to the collision-frame z-axis, which, as discussed in section 3, is coincident with Vj i, the initial relative velocity vector. If the electric field vector of the pump laser, which defines the laboratoiy-fixed Z axis, is chosen to lie parallel to Vi i(Fig. 3), and if we consider a P<- S excitation process, then, as discussed in section 3, only the P =o(ij=l ttij=0>) atomic state is prepared [13-15,31]. Since Z and Vj i are coincident pnor to the collision, the collision-frame and laboratory-frame z-axes are identical This we shall refer to as parallel... 

FIGURE 10. Absolute value of the <1 H 2> and <1 H 4> coupling matrix elements in the asymptotic uncoupled basis defined by Eq. 38. The curves were calculated using the Z, 11 and 3f[ potential curves shown in Fig. 1 for an oibital angular momentum of i2=55 and assuming a mixing angle of 0=18.4 (sin OsO.l). The dashed curve corresponds to the difference between the W (R) and lWjj(R) potential curves. Fig. 9 and Fig. 10 differ only in the value of the orbital an ar momentum. Note that the curve for the <1,, H 2> matrix element has been multiplied by 1(X) here. 

Multiplicity associated with angular momentum is always two times the value plus one. The multiplicity of orbital angular momentum is 2/+ 1. The total intrinsic spin multiplicity is 25 + 1, and the resultant multiplicity of the oibital-spin coupling angular momentum is 2J + 1. Spin multiplicities of 1, 2, 3, and 4 are called singlet, doublet, triplet, and quartet respectively. For the current example of the excited electronic state of lithium, the three nonequivalent electrons may be coupled to form a quartet state (5 = 3/2) ... 

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