For one particle in three dimensions, its units are (length) − 3/2, so that an integral of over a region of three-dimensional space is a unitless probability (the probability that the particle is in that region).
For one particle in three dimensions, its units are (length) − 3/2. These unusual units are required so that an integral of over a region of three-dimensional space is a unitless probability (the probability that the particle is in that region).