Analytical solutions to differential equations in the form of ÿ+[q(t)+q1(t)]y=0 are presented, where q1(t) is dependent on the solution of the basic equation ÿ+q(t)y=0. Various forms of the first equation are generated through a suggested procedure and their solutions should have some value in the mathematical physics field as well as in engineering applications.

The solid harmonic yLM[(r1Λr2)Λr3] was expressed in terms of the spherical harmonics YL1M1(r̂1), YL2M2(r̂2), and YL3M3(r̂3), where the coefficients of the expansion were expressed in terms of 9j symbols. Here we present a simpler form of those coefficients expressed in terms of 6j symbols.

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The radial part of the matrix element of Goldhammer's Hamiltonian is expressed in the integral form. The variation principle is applied to give the maximum binding energy of the nuclear system. This results in a set of Morpurgo type coupled differential equations corresponding to each quantum of excitation.

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