Elements of Non-relativistic Quantum MechanicsThis book presents the basic structure of quantum mechanics, the elements needed to properly understand the subject and its applications. It is written at a level which is intermediate between the standard graduate textbooks, which it intends to supplement, and the more advanced mathematical writings in the subject. Particular attention is given to the concepts of kinematical and dynamical symmetries. The unifying thread that links the study of particles and systems of particles is the connection between Galilean invariance and the fundamental observables of a system. The mathematical appendices on the Hilbert space, the theory of distributions and Dirac's formalism provide a mathematical basis which is adequate for many working theoretical physicists. |
Contents
INTRODUCTION | 1 |
STATES AND OBSERVABLES | 10 |
COMMENSURABILITY | 30 |
DYNAMICS | 40 |
A PARTICLE IN ONE DIMENSION | 62 |
the harmonic oscillator | 98 |
A SPINLESS PARTICLE IN THREE DIMENSIONS | 106 |
DYNAMICAL SYMMETRIES AND CONSERVATION LAWS | 133 |
SYSTEMS COMPOSED OF DIFFERENT SUBSYSTEMS | 175 |
SYSTEMS OF IDENTICAL PARTICLES | 202 |
APPENDIX A FINITEDIMENSIONAL VECTOR SPACES | 234 |
APPENDIX B THE HILBERT SPACE | 264 |
DIRACS FORMULATION IN THE HILBERT SPACE | 281 |
A REMINDER FROM CLASSICAL MECHANICS | 312 |
NOTES | 320 |
328 | |
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Common terms and phrases
angular momentum antiunitary arbitrary basis vectors beam belonging called Chapter classical mechanics commutation relations configuration coordinates corresponding defined definition denote detector determine Dirac's distribution dynamical symmetry eigenprojections eigensubspace eigenvalue equation eigenvectors elements equivalent example experiment experimental setup expression field gradient finite-dimensional follows function space fundamental set galilean invariance galilean transformations given hamiltonian Heisenberg Heisenberg picture hermitean operator Hilbert space identical integral irreducible set linear operator magnets matrix maximal measurement maximal observable measurement apparatus notation obtain orthogonal orthonormal basis permutation phase factor preparation apparatus pure quantum mechanics reference representation respectively rotation scalar product Schrödinger Schrödinger picture Section set of observables single-particle space H spectral family spectral resolution spectrum spin components spinless particle Stern-Gerlach subspace subsystems tensor product test functions theorem theory unit vectors unitary operator unitary space variable vector space verify write written yields zero