## Lectures on Quantum MechanicsThese are the lecture notes from a two-semester graduate course and a two-semester undergraduate course taught by the author. The lectures are arranged in a logical manner and reflect the informality of the classroom. Each topic is explained with several examples so that the ideas develop naturally, which is immensely helpful to students. The book is self-contained; most of the steps in the development of the subject are derived in detail and integrals are either evaluated or listed when needed. The motivated student can work through the notes independently and without difficulty. The book is suitable for graduate students in mathematics or advanced undergraduates in physics interested in an introduction to quantum mechanics. |

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### Contents

Review of Classical Mechanics | 1 |

Review of Essential Mathematics | 16 |

Basics of Quantum Mechanics | 58 |

Copyright | |

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angular momentum operator approximation arbitrary basis calculate center of mass classical mechanics coefficients commutation relations components coordinates corresponding Coulomb definition degeneracy delta function depends derivatives determine diagonal differential dimensional dimensions Dirac Dirac delta function eigenstates eigenvalues eigenvectors electron energy eigenvalues example expectation value finite follows Furthermore given Green's function ground state energy Hamiltonian harmonic oscillator Hermitian Hilbert space hydrogen atom implies independent infinite infinitesimal invariant known Lagrangian leads Let us assume Let us consider Let us note linear momenta motion namely normalization constant obtain parameter parity Pauli matrices perturbation physical Poisson bracket polynomials potential probability probability amplitude quantum mechanics quantum numbers radial region right hand side rotation satisfy scattering cross section Schrodinger equation Similarly solution solve spherical spin symmetry theorem theory tonian trajectory transformation trial wave function vanishes variables vector wave function write zero