In addition to l and m, a third integer n > 0, emerges from the boundary conditions placed on R. The functions R and Y that solve the equations above depend on the values of these integers, called quantum numbers. It is customary to subscript the wave functions with the values of the quantum numbers they depend on. The final expression for the normalized wave function is: ψ ψ n ℓ ℓ m = R n ℓ ℓ ( r ) Y ℓ ℓ m ( θ θ , ϕ ϕ ) R n ℓ ℓ ( r ) = ( 2 Z n a μ μ ) 3 ( n − − ℓ ℓ − − 1 ) ! 2 n ( n + ℓ ℓ ) ! e − − Z r / n a μ μ ( 2 Z r n a μ μ ) ℓ ℓ L n − − ℓ ℓ − − 1 ( 2 ℓ ℓ + 1 ) ( 2 Z r n a μ μ ) where: