The two-body Schrodinger equation

The Schrodinger equation (1.2) can be solved by separating variables. Writing 

Many other useful forms have been proposed (Steele and Lippincott, 1962) and their parameters were related to spectroscopic constants as will be given for the Morse potential by Eq. (1.14). Quite often, the potential V(r) is expanded as a power series in the displacement from equilibrium (force field method) 

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For pedagogical reasons, we shall start this review with very elementary reminders of the two-body problem, followed by some mathematical developments on the two-body Schrodinger equation, which will be useful for their three-body analogues discussed in chapters 8,9 and 10. The three-body problem... 

Though the two-body Schrodinger equation is separable, that is, r(r, 0, ( )) = Y (0, < >)R r), it is important that the radial equation. Equation 9.22, is still connected with the angular part of the problem. It incorporates the angular momentum quantum number /, and thus Equahon 9.22 really represents an infinite number of differential equahons corresponding to the infinite possible choices of / (namely, 0,1,2,...). Hence, any radial function, R r), found from solving Equation 9.22 will ultimately have to be labeled with, and distinguished by, the I value. 

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