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- W158949367 abstract "In this chapter, after a review of the mathematical and physical foundations of quantum mechanics, we introduce the approximation methods needed in the applications. In the first place, we introduce the variational method arising from Rayleigh’s variational principles, which gives upper bounds to energy of ground and excited states. Non-linear variational parameters in the approximate wavefunction are optimized by the Ransil’s method, while linear parameters in the Ritz’s method are optimized through diagonalization of the matrix representative of the Hamiltonian over a given basis of regular functions. Next, different perturbative methods for stationary states are considered, starting from Rayleigh–Schroedinger perturbation theory, where special attention is deserved to the efficient pseudostate method giving bounds to second-order quantities, up to Brillouin–Wigner and Epstein–Nesbet theories, symmetry-adapted theories including exchange, and the recently developed moment method. A glance at the Wentzel–Kramers–Brillouin method useful in one-dimensional quantum mechanical problems concludes the chapter." @default.
- W158949367 created "2016-06-24" @default.
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- W158949367 date "2013-01-01" @default.
- W158949367 modified "2023-09-26" @default.
- W158949367 title "Mathematical foundations and approximation methods" @default.
- W158949367 doi "https://doi.org/10.1016/b978-0-444-62647-9.00001-4" @default.
- W158949367 hasPublicationYear "2013" @default.
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