The wavefunctions of the composite particle representation theory (CPRT) are composed of two parts, the fermion part and the composite particle part. The CPRT wavefunction's fermion part is identical to the shell model (SM) wavefunction. The composite particle degrees of freedom exist in the O's form, so a criterion to identify physical states is presented. The formulas of the CPRT wavefunction's normalization are also presented explicitly. Calculating the normalizations is another effective way to identify physical states. As a test for CPRT the ground state's CPRT wavefunctions for the s-d shell nuclei 20O and 20F as well as their normalizations are calculated. These strict numerical results show that the composite particle representation is equivalent to the conventional representation in quantum mechanics.