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New exact analytical bound-state solutions of the D-dimensional Klein-Gordonequation for a large set of couplings and potential functions are obtained viamapping onto the nonrelativistic bound-state solutions of the one-dimensionalgeneralized Morse potential. The eigenfunctions are expressed in terms ofgeneralized Laguerre polynomials, and the eigenenergies are expressed in termsof solutions of irrational equations at the worst. Several analytical resultsfound in the literature, including the so-called Klein-Gordon oscillator, areobtained as particular cases of this unified approach

New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential