From Classical to Quantum Mechanics: An Introduction to the Formalism, Foundations and Applications
Cambridge University Press, Mar 11, 2004 - Science
This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.
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algebra amplitude angular momentum asymptotic atom canonical central potential classical coefficients commutation relations consider constant coordinates corresponding deﬁned deﬁnition denoted density density matrix derivative differential equation differential operators Dirac dynamical eigenfunctions eigenvalue eigenvectors electron energy evaluate ﬁnds ﬁrst first-order formalism formula Fourier frequency given Hamilton–Jacobi equation Hamiltonian operator harmonic oscillator hence Hilbert space implies integral interaction invariant Lagrangian leads linear magnetic matrix momentum operators Moreover motion obtained parameter particle Pauli equation perturbation phase space photon physical Poincaré group Poisson bracket potential problem properties quantization quantum mechanics radiation representation result rotation scalar scattering Schrödinger equation self-adjoint operators space H spectrum spin stationary sub-space symmetry symplectic theorem theory tion transformation unitary unitary operator vanishes variables vector field velocity virtue wave equation wave function wave packet Weyl