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Consider the Hermiticity of the following operators. Prove that the momentum operator is Hermitian. For simplicity you may perform this proof for a one-dimensional system (i.e., only consider functions of x. and consider only the P operator). Is the operator d/dx Hermitian? Prove your answer. Is the operator d^2/dx^2 Hermitian? Prove your answer. Is the operator H = - h^2/2m d^2/dx^2 + V(x) Hermitian if V(x) is real? Prove your answer.

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h d\ni dr\nThe momentum operator isp - i\nTo show that\nConsider,\nTherefore, themomentum operator is hermitian\nThe given operator

The Hamiltonian operator is given bv\n2m dx\nTo show that\nKfax\nConsider,\n2m dx2\n.; [f4I.ng浩dr -li:&.삐\n2mdx\n0-1 0\nTherefore, the

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