We analyze the simulation result of non-interacting scalar eld dark matter halos using energy eigenfunction expansion. The scalar eld dark matter obeys the Poisson-Schrodinger (SP) equation. At late time, when the dark matter halos are virialized, we can solve time independent Schrodinger equation and obtain amplitude of each eigenmode. We nd that the distribution function (DF) of the dark matter halos can be described by models of classical distribution functions, and we develop a method to solve potential and density of a spherically symmetric Schrodinger-Poisson system whose distribution function obeys fermionic King model. Also, we construct arti cial dark matter halos using di erent potentials, and test their stability. The amplitudes of the arti cial halos are generated by fermionic King model.