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**Mathematical methods in quantum mechanics. With applications to Schrödinger operators.
2nd ed.**
*(English)*
Zbl 1342.81003

Graduate Studies in Mathematics 157. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1704-8/hbk). xiv, 358 p. (2014).

This is the second edition of a textbook introducing to the necessary mathematical background of operator theory for quantum mechanics. For a review of the first edition see [the author, Mathematical methods in quantum mechanics. With applications to Schrödinger operators. Providence, RI: American Mathematical Society (AMS) (2009; Zbl 1166.81004)]. Besides corrections of misprints in the first edition which are listed on http://www.mat.univie.ac.at/~gerald/ftp/book-schroe/errata.pdf, the author has adapted suggestions by colleages and students. Chapter 3, “The spectral theorem”, has been reworked for to be easier to understand by students. Proofs in Section 9.4, “Inverse spectral theory”, have been simplified. Eventually, the appendix on measure theory has been extended to include more examples and a formula for changes of variables. Misprints in the second edition are listed on http://www.mat.univie.ac.at/~gerald/ftp/book-schroe/errata2.pdf.

Reviewer: K.-E. Hellwig (Berlin)

### MSC:

81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |

81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |

81Q15 | Perturbation theories for operators and differential equations in quantum theory |

47B25 | Linear symmetric and selfadjoint operators (unbounded) |

47B15 | Hermitian and normal operators (spectral measures, functional calculus, etc.) |

46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |

46C07 | Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) |

28A25 | Integration with respect to measures and other set functions |

46G12 | Measures and integration on abstract linear spaces |