​​Do​​Ne[r_]:=
1
4
1-
2
αn
-(-1+2
2
αl
+
2
αn
)Cos[2r]-
2
(-1+2
2
αl
+
2
αn
+(-1+
2
αn
)Cos[2r])
+16αlαnConjugate[αl]Conjugate[αn]Cos[r]Cos[Conjugate[r]]
;​​,{αn,0,1,0.01},{αl,0,1,0.01}​​​​ListPlot3DTable[-2Ne[Pi/4]&&(αn^2+αl^2)<1,{αn,0,1,0.01},{αl,0,1,0.01}],DataRange{{0,1},{0,1}},PlotRangeAll,AxesLabel{Style["
α
l
",10,Bold,Black],Style["
α
n
",10,Bold,Black],Style["N",10,Bold,Black]},PlotLabel"r=
π
4
"