THEORETICAL PHYSICS 2

By JENNIFER BROWN

CONTENTS OPERATOR METHODS IN QUANTUM MECHANICS INTRODUCTION MATHEMATICAL FOUNDATIONS HILBERT SPACE THE SCHWARTZ INEQUALITY SOME PROPERTIES OF VECTORS IN A HILBERT SPACE ORTHONORMAL SYSTEMS OPERATORS ON HILBERT SPACE EIGENVECTORS AND EIGENVALUES OBSERVABLES GENERALISED UNCERTAINTY PRINCIPLE 1110 BASIS TRANSFORMATIONS 1111 MATRIX REPRESENTATION OF OPERATORS 1112 MATHEMATICAL INTERLUDE: DIRAC DELTA FUNCTION 1113 OPERATORS WITH CONTINUOUS OR MIXED (DISCRETE-CONTINUOUS) SPECTRA APPLICATIONS HARMONIC OSCILLATOR DELTA-FUNCTION POTENTIAL WELL INTRODUCTION TO SECOND QUANTISATION VIBRATING STRING QUANTISATION OF VIBRATING STRING GENERAL SECOND QUANTISATION PROCEDURE ANGULAR MOMENTUM ORBITAL ANGULAR MOMENTUM EIGENVALUES OF ORBITAL ANGULAR MOMENTUM EIGENFUNCTIONS OF ORBITAL ANGULAR MOMENTUM MATHEMATICAL INTERLUDE: LEGENDRE POLYNOMIALS AND SPHERICAL HARMONICS ANGULAR MOMENTUM AND ROTATIONAL INVARIANCE SPIN ANGULAR MOMENTUM SPINORS ADDITION OF ANGULAR MOMENTA ADDITION OF SPIN 2 OPERATORS 2 AND ORBITAL ANGULAR MOMENTUM GENERAL CASE APPROXIMATION METHODS FOR BOUND STATES VARIATIONAL METHODS VARIATIONAL THEOREM INTERLUDE : ATOMIC UNITS HYDROGEN MOLECULAR ION, H+ GENERALISATION: RITZ THEOREM LINEAR VARIATION FUNCTIONS PERTURBATION METHODS TIME-INDEPENDENT PERTURBATION THEORY TIME-DEPENDENT PERTURBATION THEORY JWKB METHOD DERIVATION CONNECTION FORMULAE *JWKB TREATMENT OF THE BOUND STATE PROBLEM BARRIER PENETRATION ALPHA DECAY OF NUCLEI SCATTERING THEORY SPHERICALLY SYMMETRIC SQUARE WELL MATHEMATICAL INTERLUDE BRIEF REVIEW OF COMPLEX ANALYSIS PROPERTIES OF SPHERICAL BESSEL/NEUMANN FUNCTIONS EXPANSION OF PLANE WAVES IN SPHERICAL HARMONICS THE QUANTUM MECHANICAL SCATTERING PROBLEM BORN APPROXIMATION *FORMAL TIME-INDEPENDENT SCATTERING THEORY *LIPPMANN-SCHWINGER EQUATION IN THE POSITION REPRESENTATION *BORN AGAIN! IDENTICAL PARTICLES IN QUANTUM MECHANICS MULTI-PARTICLE SYSTEMS PAULI EXCLUSION PRINCIPLE REPRESENTATION OF ?(1, 2, , N) NEGLECTING THE SYMMETRY OF THE MANY-BODY WAVE FUNCTION FERMIONS BOSONS EXCHANGE FORCES HELIUM ATOM GROUND STATE HYDROGEN MOLECULE SCATTERING OF IDENTICAL PARTICLES SCATTERING OF IDENTICAL SPIN ZERO BOSONS SCATTERING OF FERMIONS *MODERN ELECTRONIC STRUCTURE THEORY *THE MANY-ELECTRON PROBLEM *ONE-ELECTRON METHODS *HARTREE APPROXIMATION *HARTREE-FOCK APPROXIMATION *DENSITY FUNCTIONAL METHODS *SHORTCOMINGS OF THE MEAN-?ELD APPROACH *QUANTUM MONTE CARLO METHODS DENSITY OPERATORS PURE AND MIXED STATES PROPERTIES OF THE DENSITY OPERATOR DENSITY OPERATOR FOR SPIN STATES DENSITY OPERATOR IN THE POSITION REPRESENTATION DENSITY OPERATOR IN STATISTICAL MECHANICS DENSITY OPERATOR FOR A FREE PARTICLE IN THE MOMENTUM REPRESENTATION DENSITY OPERATOR FOR A FREE PARTICLE IN THE POSITION REPRESENTATION *DENSITY MATRIX FOR THE HARMONIC OSCILLATOR