05865fam a2200265 a 45000010008000000030008000080050017000160080041000330100017000740200015000910350020001060350023001260350017001490400035001660500024002010820020002251000024002452450051002692500012003202600038003323000036003705040051004065055122004576500020055791521836BD-DhUL20140916095148.0940707s1994    nyua     b    001 0 eng    a   94026837   a0306447908  a(OCoLC)30811075  a(OCoLC)ocm30811075  a(NNC)1521836  aDLCcBD-DhULdBD-DhULdOrLoB-B00aQC174.12b.S52 199400a530.12220bSHP1 aShankar, Ramamurti.10aPrinciples of quantum mechanics /cR. Shankar.  a2nd ed.  aNew York :bPlenum Press,cc1994.  axviii, 676 p. :bill. ;c27 cm.  aIncludes bibliographical references and index.00g1.tMathematical Introduction --g1.1.tLinear Vector Spaces: Basics --g1.2.tInner Product Spaces --g1.3.tDual Spaces and the Dirac Notation --g1.4.tSubspaces --g1.5.tLinear Operators --g1.6.tMatrix Elements of Linear Operators --g1.7.tActive and Passive Transformations --g1.8.tThe Eigenvalue Problem --g1.9.tFunctions of Operators and Related Concepts --g1.10.tGeneralization to Infinite Dimensions --g2.tReview of Classical Mechanics --g2.1.tThe Principle of Least Action and Lagrangian Mechanics --g2.2.tThe Electromagnetic Lagrangian --g2.3.tThe Two-Body Problem --g2.4.tHow Smart Is a Particle? --g2.5.tThe Hamiltonian Formalism --g2.6.tThe Electromagnetic Force in the Hamiltonian Scheme --g2.7.tCyclic Coordinates, Poisson Brackets, and Canonical Transformations --g2.8.tSymmetries and Their Consequences --g3.tAll Is Not Well with Classical Mechanics --g3.1.tParticles and Waves in Classical Physics --g3.2.tAn Experiment with Waves and Particles (Classical) --g3.3.tThe Double-Slit Experiment with Light --g3.4.tMatter Waves (de Broglie Waves) --g4.tThe Postulates - a General Discussion --g4.1.tThe Postulates --g4.2.tDiscussion of Postulates I-III --g4.3.tThe Schrodinger Equation (Dotting Your i's and Crossing your h's) --g5.tSimple Problems in One Dimension --g5.1.tThe Free Particle --g5.2.tThe Particle in a Box --g5.3.tThe Continuity Equation for Probability --g5.4.tThe Single-Step Potential: a Problem in Scattering --g5.5.tThe Double-Slit Experiment --g5.6.tSome Theorems --g6.tThe Classical Limit --g7.tThe Harmonic Oscillator --g7.1.tWhy Study the Harmonic Oscillator? --g7.2.tReview of the Classical Oscillator --g7.3.tQuantization of the Oscillator (Coordinate Basis) --g7.4.tThe Oscillator in the Energy Basis --g7.5.tPassage from the Energy Basis to the X Basis --g8.tThe Path Integral Formulation of Quantum Theory --g8.1.tThe Path Integral Recipe --g8.2.tAnalysis of the Recipe --g8.3.tAn Approximation to U(t) for the Free Particle --g8.4.tPath Integral Evaluation of the Free-Particle Propagator --g8.5.tEquivalence to the Schrodinger Equation --g8.6.tPotentials of the Form V = a + bx + cx[superscript 2] + dx + exx --g9.tThe Heisenberg Uncertainty Relations --g9.2.tDerivation of the Uncertainty Relations --g9.3.tThe Minimum Uncertainty Packet --g9.4.tApplications of the Uncertainty Principle --g9.5.tThe Energy-Time Uncertainty Relation --g10.tSystems with N Degrees of Freedom --g10.1.tN Particles in One Dimension --g10.2.tMore Particles in More Dimensions --g10.3.tIdentical Particles --g11.tSymmetries and Their Consequences --g11.1.tOverview --g11.2.tTranslational Invariance in Quantum Theory --g11.3.tTime Translational Invariance --g11.4.tParity Invariance --g11.5.tTime-Reversal Symmetry --g12.tRotational Invariance and Angular Momentum --g12.1.tTranslations in Two Dimensions --g12.2.tRotations in Two Dimensions --g12.3.tThe Eigenvalue Problem of L[subscript z] --g12.4.tAngular Momentum in Three Dimensions --g12.5.tThe Eigenvalue Problem of L[superscript 2] and L[subscript z] --g12.6.tSolution of Rotationally Invariant Problems --g13.tThe Hydrogen Atom --g13.1.tThe Eigenvalue Problem --g13.2.tThe Degeneracy of the Hydrogen Spectrum --g13.3.tNumerical Estimates and Comparison with Experiment --g13.4.tMultielectron Atoms and the Periodic Table --g14.tSpin --g14.2.tWhat is the Nature of Spin? --g14.3.tKinematics of Spin --g14.4.tSpin Dynamics --g14.5.tReturn of Orbital Degrees of Freedom --g15.tAddition of Angular Momenta --g15.1.tA Simple Example --g15.2.tThe General Problem --g15.3.tIrreducible Tensor Operators --g15.4.tExplanation of Some "Accidental" Degeneracies --g16.tVariational and WKB Methods --g16.1.tThe Variational Method --g16.2.tThe Wentzel-Kramers-Brillouin Method --g17.tTime-Independent Perturbation Theory --g17.1.tThe Formalism --g17.2.tSome Examples --g17.3.tDegenerate Perturbation Theory --g18.tTime-Dependent Perturbation Theory --g18.1.tThe Problem --g18.2.tFirst-Order Perturbation Theory --g18.3.tHigher Orders in Perturbation Theory --g18.4.tA General Discussion of Electromagnetic Interactions --g18.5.tInteraction of Atoms with Electromagnetic Radiation --g19.tScattering Theory --g19.2.tRecapitulation of One-Dimensional Scattering and Overview --g19.3.tThe Born Approximation (Time-Dependent Description) --g19.4.tBorn Again (The Time-Independent Approximation) --g19.5.tThe Partial Wave Expansion --g19.6.tTwo-Particle Scattering --g20.tThe Dirac Equation --g20.1.tThe Free-Particle Dirac Equation --g20.2.tElectromagnetic Interaction of the Dirac Particle --g20.3.tMore on Relativistic Quantum Mechanics --g21.tPath Integrals - II --g21.1.tDerivation of the Path Integral --g21.2.tImaginary Time Formalism --g21.3.tSpin and Fermion Path Integrals.g21.4.tSummary --tApp. A.1. Matrix Inversion --tApp. A.2. Gaussian Integrals --tApp. A.3. Complex Numbers --tApp. A.4. The i[epsilon] Prescription. 0aQuantum theory.