The behaviours of the charged particles moved in a crystal channel have been controlled by the interaction potential between a charged particles and the crystal.Usual interaction potential is Lindhard potential

Moliere potential and Sine-square potential.The interaction potential between a electron and a crystal may be described by ch

-2

x potential if particle moved in the channel with the lower index.In the frame of quantum mechanics

Schrodinger equation has been deduced to the hypergeometric equation by this potential.The eigenvalue and the eigefunction problem of the system have been transformed to the eigenvalue and the eigefunction problem of the hypergeometric equation.The relativistic effect and Doppler effect are considered.The eigenvalue and the eigefunction have been calculated

the level distribution and the spectral distribution are induced.As example

the planar channeling radiation of a electron in channel of Si(110) is considered

if the parameters related to particle and the crystal have been chosen.If chosing the distance α=0.096 nm between the crystal surfase

the deep of the potential well

V

0

=27 eV

the electron energy

E

=5.0 GeV

transition between nearby level has been calculated

and the radiation energy Δ

E

=49.1 MeV has been obtained.It shows that conformity between the theory and the experiment is better.