Time evolution of a non-stationary state

Infinite square well

ψ[x_,n_,a_]:=Sqrt[2/a]Sin[n Pi x/a]

ψQ[x_,t_,c1_,ϕ_,n1_,n2_]:=Module[{ψ1,ψ2,c2},
ψ1=ψ[x,n1,10];ψ2=ψ[x,n2,10];c2=Sqrt[1-c1^2];c1^2 ψ1^2 +c2^2 ψ2^2 +2c1 c2 ψ1 ψ2 Cos[(n1^2-n2^2)t+ϕ] 
]

Scaled for a nucleon in a nucleus

Manipulate[Plot[ψQ[x,t,c,ϕ,n1,n2],{x,0,10},PlotRange->{0,0.4},AxesLabel->{"x(fm)",None},BaseStyle->FontSize->14,PerformanceGoal->"Quality",Epilog->{Text["time*(10^22) s",{5,0.37}]}],{{t,0},0,5},{{c,0.707},0,1},{{ϕ,0},0,2Pi},{{n1,1},1,20,1},{{n2,2},{1,2,3,4,10,20,50} }]