> restart; > > with(PDEtools); > > with(Units[Standard]); > with(ScientificConstants); > > # > > # Electron velocity distribution: > > f[e] := A[e]*exp(-B[e]*(((1/2)*m[e]*v^2)^2+((1/2)*m[e]*v^2*m[e])*`ϖ`^2*lambda[e]^2)/T[e]^2); > f[e, 1] := f[e]/A[e]; > > f[e, 2] := (1/2)*f[e, 1]*m[e]*v^2; > expr[e, 1] := `assuming`([4*Pi*(int(f[e, 1]*v^2, v = 0 .. infinity))], [positive]); > expr[e, 2] := `assuming`([4*Pi*(int(f[e, 2]*v^2, v = 0 .. infinity))], [positive]); > expr[e, lhs] := simplify(expr[e, 1]/expr[e, 2]); > expr[e, rhs] := 1/T[e]; > eq[e, 1] := expr[e, lhs]/expr[e, rhs] = 1; > > # Constants: > `ϖ` := 22*10^6*Unit('Hz'); > T[e] := 3*Unit('eV'); > lambda[e] := Unit('mm'); > m[e] := evalf(Constant(m[e], units)); > > eq[e, 2] := simplify(eq[e, 1]); > B[e] := fsolve(eq[e, 2], B[e]); > A[e, res1] := simplify(1/expr[e, 1]); > A[e, res2] := simplify(T[e]/expr[e, 2]); >