Recent content by John Finn

Suppose you take a Schroedinger-like equation $$-\psi''+F(x)\psi=0$$. (E.g. F(x)=V(x)-E, and not worried about factors of 2 etc.) This is positive definite if $$\int \left( \psi'^2+F(x)\psi^2 \right)dx>0$$. Is so, you can write this as the product $$(d/dx+g(x))(-d/dx+g(x))\psi=0$$, i.e. as...

I am interested in theoretical physics and applied math. Many questions I have in the math area are along the lines of "I see how to do it, but is this really useful, important, connected to other areas, etc?"

I know that linear control theory, in the form ##\dot{x}=Ax+Bu##, ##\dot{u}=Cx+Du##, can be put in the form of a matrix Riccati equation. But is there really an advantage to doing so?

This brings up a related issue. One can iterate a Markov chain $p(i,t+1)=\sum_j T_{i,j) p(j,t)$ from $t=0$ to $t=N$, i.e. in vector form $p(t+1)=T p(t)$ and then make the measurement $c=(q(N),p(N))$, where $(\cdot , \cdot)$ is the $l^2$ inner product. Or you could advance the measurement vector...