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Science · Advanced Physics
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Opg 3 The movement of an electron inside a hydrogen atom is described by the Hamiltonian operator where me is the mass of the electron and r is the distance between the electron and the proton. We use the notation ψη1m for the eigenstates with main quantum number n, angular momentum quantum number, and magnetic quantum number m. Spin is neglected. Throughout the whole exercise we only consider the subspace with main quantum number n 2, described by the base {200, /211,/210, 1>21-13. At some time, the wavefunction in this basis is given by 2 4i where N is a positive constant. a) c) d) Calculate the mean and the standard deviation of the operator Lz for the state ψ The hydrogen atom is now exposed to a perturbation H = α(碌+ Ls), where α is a positive constant. Use 1.-order perturbation theory to find the energy shifts on the subspace with main quantum number n 2, and find the corresponding eigenfunctions. Hint: express H by L2 and Lz

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