content_image/342581.jpg content_image/342578.jpg content_image/342577.jpg content_image/342576.jpg content_image/342575.jpg content_image/342574.jpg content_image/342573.jpg
and r$_{max}$ defined by (2.14) and (2.15) we find 

<img src='content_image/342581.jpg'>

where Jc κ 2 ( 3 κ 2 2 E ) 3 2 = 1 refers to the motion in a circle, 0 < Jc κ 2 ( 3 κ 2 2 E ) 3 2 < 1 corresponds to the motion between two circles, and Jc κ 2 ( 3 κ 2 2 E ) 3 2 = 0, i.e. J = 0 is the condition for the motion in the segment. 

## III. QUANTUM MECHANICS OF THE RELATIVISTIC MASSLESS HAR- MONIC OSCILLATOR 

In relativistic quantum mechanics the massless harmonic oscillator defined by the Hamil- tonian (2.1) is described by a massless version of the spinless Salpeter equation 

where Δ$_{x}$ = ( ∂ ∂ $_{x}$) $^{2}$. Therefore the eigenvalue equation for the Hamiltonian ˆ Hψ$_{E}$ = Eψ$_{E}$ takes the form of the pseudodifferential equation 

Performing the Fourier transformation 

we get from (3.2) the following equation: 

<img src='content_image/342578.jpg'>

<img src='content_image/342577.jpg'>

<img src='content_image/342576.jpg'>

<img src='content_image/342575.jpg'>

where Δ$_{k}$ = ( ∂ ∂ $_{k}$) $^{2}$. Finally, switching over to the spherical coordinates k = ( k sin α cos β, k sin α sin β, k cos α ), where k = | k | , and making the ansatz 

<img src='content_image/342574.jpg'>

where Y m l ( α, β ) are the spherical functions, we obtain the “radial equation” 

<img src='content_image/342573.jpg'>

