Quantum mechanics by split quaternions

In this study, after defining of quaternion and split quaternion, their matrix representations and properties are defined. The basic of split quaternion are equalized to Pauli-spin matrices. Non relativist quantum theory is discussed by split quaternions. Also, Pauli operators and Pauli observable are defined by split quaternions and spin vector is represented by split quaetrnions. Timelike quaternions can be used for defining of rotations. At the end of study, the action of particale in magnetic field is attained by Hamilton?s operator and split quaternions. Keywords: Quaternion, split quaternion, Non-relativistic quantum theory, particle in magnetic field, spinor, Pauli-spin matrices.