STRONG UNIQUE CONTINUATION OF THE SCHR$\"{O}$DINGER OPERATOR

It is well known that if P(x,D) is an elliptic differential operator, with real analytic coefficients, and P(x,D)u = 0 in an open, connected subset .ohm..mem.R$^{n}$ , then u is real analytic in .ohm. Hence, if there exists x$_{0}$ .mem..ohm. such that u vanishes of .inf. order at x$_{0}$ , u must be identically 0. If a differential operator P(x, D) has the above property, we say that p(x,D) has the strong unique continuation property (s.u.c.p.). If, on the other hand, P(x,D)u = 0 in .ohm., and u = 0 in .ohm.', an open subset of .ohm., implies that u = 0 in .ohm. we say that P(x,D)u = 0 in .ohm., and suppu .contnd. K .contnd. .ohm implies that u = 0 in .ohm. we sat that P(x,D) has the weak unique continuation property (m.u.c.p.).