Plot eq. 9.26, energy for two level, weak periodic potential.

ϵ = (1/2)((Subscript[(ϵ^0), q])- (Subscript[(ϵ^0), q - K])) ± ((( (1/4)((((Subscript[(ϵ^0), q])- (Subscript[(ϵ^0), q - K])))^2) + |(Subscript[U, k])(|^2)))^(1/2)),

or

((2m)/ℏ) ϵ = (1/2)( (q^(2 ))+ (((q - K))^2)   ± ((( ((((q^(2 ))- (((q - K))^2)))^2) + 4 ((((ℏ/(2m))))^2)|(Subscript[U, k])(|^2)))^(1/2))), where

 ((((q^(2 ))- (((q - K))^2)))^2) ≫  ((((ℏ/(2m))))^2)|(Subscript[U, k])(|^2).

(* write, u =  ((((ℏ/(2m))))^2)\[LeftBracketingBar](Subscript[U, k])(\[LeftBracketingBar]^2) = ur k ; e = ((2m)/ℏ) ϵ *)
Module[{e, minE, maxE},
minE = -0.2 ;
maxE = 2 ;
e[q_, k_, s_, u_] = (1/2)(q^2 +  (q - k)^2 + s Sqrt[(q^2 -  (q - k)^2)^2 + 4 u^2]) ;
Manipulate[
Plot[{e[q, k, 1, ur k], e[q, k, -1, ur k]}
, {q, - 0.2 k,0.7k}
,AxesLabel -> {"q", ((2m)/ℏ) ϵ}
, PlotRange -> {Automatic, {minE, maxE}}
, Ticks -> None 
, Epilog->{ Line[{{k/2, 0},{k/2, maxE}}], Text[ "K/2", {k/2, -0.1 }]}
],
{{ur, 0.1, "\!\(\*FormBox[
RowBox[{FractionBox["ℏ", 
RowBox[{"2", "m", 
StyleBox[
RowBox[{" ", 
StyleBox[" ",
FontWeight->"Plain"]}]], 
StyleBox["K",
FontWeight->"Bold"]}]], 
RowBox[{"\[LeftBracketingBar]", 
RowBox[{SubscriptBox["U", 
StyleBox["k",
FontWeight->"Bold"]], "\[LeftBracketingBar]"}]}]}],
TraditionalForm]\)"}, 0, 1, Appearance -> "Open"},
{{k, 2, "K"}, 0, 10, Appearance -> "Open"},
SaveDefinitions->True
]
]

(*<<peeters` ;
peeters`setGitDir[ "phy487\\figures" ] *)

Clear[p]
p = DynamicModule[{k=2,ur=0.05`},Plot[{e$2461[q,k,1,ur k],e$2461[q,k,-1,ur k]},{q,-0.2` k,0.7` k},AxesLabel->{"\!\(TraditionalForm\`q\)",(((2 m) ϵ)/ℏ)},PlotRange->{Automatic,{minE$2461,maxE$2461}},Ticks->None,Epilog->{Line[{{(k/2),0},{(k/2),maxE$2461}}],Text["\!\(\*\nStyleBox[\"K\",\nFontWeight->\"Bold\"]\)\!\(\*\nStyleBox[\"/\",\nFontWeight->\"Bold\"]\)\!\(\*\nStyleBox[\"2\",\nFontWeight->\"Bold\"]\)",{(k/2),-0.1`}]}]]

(*peeters`exportForLatex["qmSolidsWeakBindingNearBraggFig1", p ]*)