To our best knowledge in the case of l = 0 the solution of (3.6) is not known. For l = 0 the solution to (3.6) can be expressed by means of the Airy function Ai( x ) [20], namely where C is constant. We point out that l = 0 was also the case discussed in [6], where the recurrence was identified satisfied by coefficients of the formal power series expansion for the solution to the spinless Salpeter equation corresponding to the massive relativistic harmonic oscillator. Clearly, l = 0 refers to the vanishing angular momentum, therefore we deal in this case with the quantization of the motion of a massless particle in the segment 0 ≤ r ≤ r$_{max}$ = √$_{2}$$_{E}$ κ discussed in the previous section corresponding to the condition J = 0 (third type of the motion). Furthermore, for l = 0 the ansatz (3.5) takes the form Demanding that ˜ ψ$_{E}$ ( k ) is well defined for k = 0 we find χ (0) = 0 (compare [21] Eq. (32.11)), which leads to Ai ( − 2 E (2 cκ ℏ ) 2 3 ) = 0. This quantization condition means that the values of the energy E$_{n}$ , n = 1 , 2 , . . . , are given by zeros of the Airy function a$_{n}$ . We have Using the fact that the functions Ai( x + a$_{n}$ ) / $_{Ai}$′$_{(}$$_{a}$$_{n}$$_{),}$ n = 1 , 2 , . . . $_{, where Ai}$′$_{(}$$_{x}$$_{) designates}$ the derivative of the Airy function Ai( x ), form an orthonormal basis on the interval [0 , ∞ ) [16], we find that the normalized solutions (3.5) to (3.4) in the Hilbert space L $^{2}$( R $^{3}$, d$^{3}$k ), with l = 0 can be written as From (3.10) and (3.3) we finally obtain the normalized wave functions such that where r = | x | . As in the case of the nonrelativistic harmonic oscillator with the probability density different from zero outside the turning points, the probability density ρ$_{n}$ ( r ) = | ψ$_{n}$ ( x ) | 2 does not vanish for r > r$_{max}$ ( E$_{n}$ ), where r$_{max}$ ( E$_{n}$ ) = √$_{2}$$_{E}$ n κ , n = 1 , 2 , . . . , . However, it ψ$_{n}$ ( x ) = √ c ℏ 1 π 1 (2 cκ ℏ ) 1 3 1 $_{Ai}$′$_{(}$$_{a}$$_{n}$$_{)}$$^{1}$ r ∫ ∞ 0 dk sin kr ℏ Ai ( 2 c (2 cκ ℏ ) 2 3 k + a$_{n}$ ) , (3.11) ˜ ψ$_{n}$ ( k ) ≡ ˜ ψ$_{E}$ n ( k ) = √ c 2 π 1 (2 cκ ℏ ) 1 3 1 $_{Ai}$′$_{(}$$_{a}$$_{n}$$_{)}$$^{1}$ k Ai ( 2 c (2 cκ ℏ ) 2 3 k + a$_{n}$ ) . (3.10) 11 E$_{n}$ = − (2 cκ ℏ ) 2 3 2 a$_{n}$, n = 1 , 2 , . . . . (3.9) ˜ ψ$_{E}$ ( k ) = χ ( k ) k Y 0 ( α, β ) = 1 √$_{4}$$_{π}$ χ ( k ) k . (3.8) χ ( k ) = C Ai [ 2 c (2 cκ ℏ ) 2 3 ( k − E c ) ] , (3.7)