Math 131

1) Let P=d/dx and Q=x (i.e. (Qf)(x)=x f(x)), be the momentum and position operators defined in L2(R). Compute their commutator. ... Ae0=0, Ae(n)=sqrt(n) e(n-1). a) Prove that A is unbounded and that the domain is dense in l2(N). b) Prove that its adjoint is A*(en)=sqrt(n+1) e(n+1) (the creation operator). ... ................
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