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.