Abstract: Starting from the superposition principle, Dirac introduced complex vector space representation for quantum mechanics, leaving behind in a hash some flaws in the theory, in particular dimension discrepancy concerning the basis vector sets |x> and |p> for position operator and momentum operator, respectively. A remedy for this discrepancy was recently proposed by assigning dimension to the state vectors |x> and |p>, which is unacceptable and may bring with new confronts. Abiding by the principle of dimensionless representation for state vectors, and thus the relevant transformations, we formulate a dimensionless representation for the state vectors for position and momentum, i.e., |q>and |p>, by using the annihilation and creation operators a, a⁺, thus eliminate the problems caused by dimension discrepancy in quantum mechanics literature.