Nankai Univ, Dept Phys, Tianjin 300071, Peoples R China
; Beijing Normal Univ, Inst Low Energy Nucl Phys, Beijing 100875, Peoples R China
; Chinese Acad Sci, Grad Sch, Dept Phys, Beijing 100049, Peoples R China
; Zhejiang Univ, Inst Modern Phys, Hangzhou 310027, Peoples R China
; Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; Harbin Inst Technol, Dept Phys, Harbin 150001, Peoples R China
In this work, we employ the Bethe-Salpeter (B-S) equation to investigate the spectra of free diquarks and their B-S wave functions. We find that the B-S approach can be consistently applied to study the diqaurks with two heavy quarks or one heavy and, one light quarks, but for two light-quark systems, the results are not reliable. There are a few free parameters in the whole scenario which can only be fixed phenomenologically. Thus, to determine them, one has to study baryons which are composed of quarks and diquarks.