This paperpresentsaquantummechanicaltreatmenttostudythegrowthratecharacteristicsof
Cherenkovfree-electronlaser.Forthispurpose,webasicallyusethesingle-particlemodelinwhichthe
dynamics ofasingleelectroninthepresenceofthelaser field isanalyzed.Theinclusionsofthespace-
charge (collective)effectsareconsideredbytakingintoaccountthestaticelectric field ofneighboring
electrons inthedynamicsformulations.AnanalyticalexpressionforthegainperpassintheCherenkov
laser isderived.Itisshownthatthespace-chargeeffectsdependmainlyontheoperatingwavelength,
the electrondensity,andtheelectronbeamneutralizationduetothepossiblepresenceofpositiveions.
Wediscussthevalidityboundariesoftheinteractionmodeevolvedfromthesingle-particleregimeto
the collectiveregime.Usingquantummechanicalconcepts,we finally presentaformulaforcalculating
the inclusionofthespontaneousemissionpower.