Mathematical Methods in Quantum Mechanics pdf


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Mathematical Methods in Quantum Mechanics pdf

Mathematical Methods in Quantum Mechanics pdf : Pages 384

By Gerald Teschl

The first part covers mathematical foundations of quantum mechanics from self-adjointness, the spectral theorem, quantum dynamics (including Stone’s and the RAGE theorem) to perturbation theory for selfadjoint operators. The second part starts with a detailed study of the free Schr¨odinger operator respectively position, momentum and angular momentum operators. Then we develop Weyl–Titchmarsh theory for Sturm–Liouville operators and apply it to spherically symmetric problems, in particular to the hydrogen atom. Next we investigate self-adjointness of atomic Schr¨odinger operators and their essential spectrum, in particular the HVZ theorem. Finally we have a look at scattering theory and prove asymptotic completeness in the short range case ( book page 2 )

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