Tentative list of topics to be covered (with references):
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Introduction, quantum mechanical wave function, Born interpretation (Ch-1 & 2 of Susskind).
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EPR paradox, Entangled states, hidden variables, Bell’s inequality. (Ch-3.9 of Sakurai). GHZM experiment.
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QM in Dirac notation, Bra-Ket algebra, projection operators. Matrix representation of vectors and operators. Examples. (Ch-1 of Sakurai). Postulates (Ch-4 of R Shankar)
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Review of one dimensional examples (particle in a box, step potential, dirac delta function, periodic potential) (Ch-5 of R Shankar; Griffiths)
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1D harmonic oscillator, creation/annihilation (ladder) operators and construction of the stationary state wave functions, number operator and its eigenstates. (Ch-7 of R Shankar)
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Quantum mechanics in 2 and 3 dimensions in Cartesian coordinates. Separation of variables.
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Quantum theory of angular momentum, eigenvalues and eigenfunctions. (Ch-12 of R Shankar; Ch-3 of Sakurai)
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Schroedinger equation in spherical coordinates, Free particle solution and solutions for spherically symmetric potentials, Hydrogen atom. (Ch-13 of R Shankar)
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Quantum theory of spin angular momentum. (Ch-14 of R Shankar)
- Identical particles, exchange symmetry, conservation laws, and degeneracy, Pauli principle and its applications. Discrete symmetries. (Ch-11 of R Shankar; Ch-4 & 6 of Sakurai)