Titlebook: Basic Quantum Mechanics; Kyriakos Tamvakis Textbook 2019 Springer Nature Switzerland AG 2019 textbook quantum mechanics.textbook QM.textbo

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Inversion with Partial EvaluationMany particle systems and in particular Systems of Identical Particles are considered. The Symmetrization Postulate is introduced and the classification of particles into Bosons and Fermions is derived. The Exclusion Principle for Fermions is analyzed. Composite particles are discussed.

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Applications to Finite Element MatricesMolecules as composite structures of more than one nuclei and electrons are considered and the Born-Oppenheimer method for the formulation of their eigenvalue problem is analyzed. As an example of a simple molecule the Hydrogen Ion is considered and its ground state energy is estimated.

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Basic Principles of Quantum Mechanics,The basic postulates of Quantum Mechanics are stated. The concept of quantum state vectors and the Hilbert space of states is introduced. The Eigenvalue Problem of Hermitian operators is analyzed. A general proof of the Heisenberg Uncertainty inequality is given. The position and momentum representations of the system of a particle are analyzed.

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Eigenstates of the Angular Momentum,The Angular Momentum eigenvalue problem is solved and the angular momentum eigenvalues are determined. The angular momentum eigenfunctions in the position representation (Spherical Harmonics) are derived and their properties analyzed.

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Addition of Angular Momenta,The general problem of the addition of two independent angular momenta is considered. The arising Clebsch-Gordan coefficients are analyzed and general formulas for them are derived.

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