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Let P^{2 }be the operator defined by Equation (5.25) and the operator defined by

With the same requirements for the functions . Show that as a consequence of (5.26) P and P^{2 }are self-adjoint operators. Are P and P^{2 }self-adjoint operators if (5.26) is not fulfilled?

Let the self-adjoint operator $H=P_{2}$ be defined by $?x?H???=?dx_{2}d_{2}??x???$ for every component $?x???$ of any $???$. In order that $Q,P$ and any power of these operators be defined in $?$, the space of components $?x???$ must be the space of continuous infinitely differentiable functions for which $?_{?a}dx?x_{n}dx_{m}d_{m}??x????_{2}<?.$ Further $?x?a???=?x??a???=0$

In science, a self-adjoint administrator on a limitless layered complex vector space V with inward item {\displaystyle \langle \cdot ,\cdot \rangle }\