In this work, we evaluate the energy spectra of baryons which consist of two heavy and one light quarks in the MIT bag model. The two heavy quarks constitute a heavy scalar or axial vector diquark. Concretely, we calculate the spectra of $|q(QQ)>_{1/2}$ and $|q(QQ)>_{3/2}$ where $Q$ and $Q$ stand for $b$ and/or $c$ quarks. Especially, for $|q(bc)>_{1/2}$ there can be a mixing between $|q(bc)_0>_{1/2}$ and $|q(bc)_1>_{1/2}$ where the subscripts 0 and 1 refer to the spin state of the diquark (bc), the mixing is not calculable in the framework of quantum mechanics (QM) as the potential model is employed, but can be evaluated by the quantum field theory (QFT). Our numerical results indicate that the mixing is sizeable
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