Titlebook: Quantum Theory for Mathematicians; Brian C. Hall Textbook 2013 Springer Science+Business Media, LLC, part of Springer Nature 2013 Hilbert

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Perspectives on the Spectral Theorem,Suppose . is a self-adjoint . × . matrix, meaning that . for all 1≤ ., . ≤ .. Then a standard result in linear algebra asserts that there exist an orthonormal basis . for . and real numbers ..,.,.. such that .. (See Theorem 18 in Chap. 8 of [24] and Exercise 4 in Chap. 7)

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The Spectral Theorem for Bounded Self-Adjoint Operators: Proofs,In this chapter we give proofs of all versions of the spectral theorem stated in the previous chapter.

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The Uncertainty Principle,In this chapter, we will continue our investigation of the consequences of the commutation relations among the position and momentum operators.

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The WKB Approximation,The WKB method, named for Gregor Wentzel, Hendrik Kramers, and Léon Brillouin, gives an approximation to the eigenfunctions and eigenvalues of the Hamiltonian operator . in one dimension.

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