Explicit expanding focusing Schrödinger lens
= Explicit expanding focusing Schrödinger lens
The initial conditions $\lambda(-1)=\sqrt{1+\eta}$ and $b(-1)=1$ select
$$
\lambda(t)=\sqrt{t^2+\eta},
\qquad b(t)=-t,
\qquad
\gamma(t)-\gamma(-1)=\int_{-1}^t\frac{d\tau}{\tau^2+\eta}.
$$
The scale grows linearly at infinity, yielding a finite critical spacetime norm for the corresponding lens solution.
= Explicit lens parameters
{synonym}