Abstract The spectrum and relativistic wave functions of B c system are investigated via solving the complete Salpeter equation. Emphases are put on the study of the partial waves of each J P state. Our study shows that there are three categories of J P states. The first category contains 0 − and 0+ states, which are 1 S 0 dominant state with a small amount of P wave and 3 P 0 dominant state with a small amount of S wave, respectively. The second category includes the natural parity states, such as 1 − , 2+, 3 − , etc. Taking the 1 − state as an example, we study it in two cases. One is the 3 S 1 dominant state with a small amount of P and D waves, and the other is the 3 D 1 dominant state but contains a large amount of S and P wave components. The third category includes the unnatural parity states, such as 1+, 2 − , 3+, etc. For the 1+ spectrum, the states are grouped into pairs with different radial quantum numbers. Each pair contains two 1 P 1 − 3 P 1 mixing states, and the corresponding mixing angles are calculated by using the relativistic wave functions.
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