By using the representation of its complex-conjugate pairs, we have investigated the diagonalization of a bounded linear operator on separable infinite-dimensional right quaternionic Hilbert space. The sufficient condition for diagonalizability of quaternionic operators is derived. The result is applied to anti-Hermitian operators, which is essential for solving Schr${\rm \ddot{o}}$dinger equation in quaternionic quantum mechanics.
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2012
American Institute of Physics
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