Feynman Path Integrals in Quantum Mechanics and Statistical Physics - Feynman Path Integrals in Quantum Mechanics and Statistical Physics -

: Path Integral Formalism Intuitive Approach Probability Amplitude Double Slit Experiment Physical State Probability Amplitude Revisit Double Slit Experiment Distinguishability Superposition Principle Revisit the Double Slit Experiment/Superposition Principle Orthogonality Orthonormality Change of Basis Geometrical Interpretation of State Vector Coordinate Transformation Projection Operator Continuous Spectrum : Matrix Representation of Linear Operators Matrix Element Linear Self-Adjoint (Hermitian Conjugate) Operators Product of Hermitian Operators Continuous Spectrum Schturm-Liouville Problem: Eigenstates and Eigenvalues Revisit Linear Self-Adjoint (Hermitian) Operators Unitary Transformation Mean (Expectation) Value and Matrix Density Degeneracy Density Operator Commutativity of Operators : Operators in Phase Space Configuration Space Position and Wave Function Momentum Space Classical Action : Transition Amplitude Path Integration in Phase Space From the Schrödinger Equation to Path Integration Trotter Product Formula Transition Amplitude Hamiltonian Formulation of Path Integration Path Integral Subtleties Mid-point Rule Lagrangian Formulation of Path Integration Complex Gaussian Integral Transition Amplitude Law for Consecutive Events Semigroup Property of the Transition Amplitude : Stationary and Quasi-Classical Approximations Stationary Phase Method/Fourier Integral Contribution from Non-Degenerate Stationary Points Unique Stationary Point Quasi-Classical Approximation/Fluctuating Path Free Particle Classical Action and Transition Amplitude Free Particle Classical Action Free Particle Transition Amplitude From Path Integrals to Quantum Mechanics Free and Driven Harmonic Oscillator Classical Action and Transition Amplitude Free Oscillator Classical Action Driven or Forced Harmonic Oscillator Classical Action Free and Driven Harmonic Oscillator Transition Amplitude Fluctuation Contribution to Transition Amplitude Maslov Correction : Generalized Feynman Path Integration Coordinate Representation Free Particle Transition Amplitude Gaussian Functional Feynman Path Integrals Charged Particle in a Magnetic Field : From Path Integration to the Schrödinger Equation Wave Function Schrödinger Equation The Schrödinger Equation’s Green’s Function Transition Amplitude for a Time-Independent Hamiltonian Retarded Green Function : Quasi-Classical Approximation Wentzel-Kramer-Brillouin (WKB) Method Condition of Applicability of the Quasi-Classical Approximation Bounded Quasi-Classical Motion Quasi-Classical Quantization Path Integral Link Potential Well Potential Barrier Quasi-Classical Derivation of the Propagator Reflection and Tunneling via a Barrier Transparency of the Quasi-Classical Barrier Homogenous Field Motion in a Central Symmetric Field Polar Equation Radial Equation for a Spherically Symmetric Potential in Three Dimensions Motion in a Coulombic Field Hydrogen Atom : Free Particle and Harmonic Oscillator Eigenfunction and Eigenvalue Free Particle Transition Amplitude for a Particle in a Homogenous Field Harmonic Oscillator Transition Amplitude Hermiticity : Matrix Element of a Physical Operator via Functional Integral Matrix Representation of the Transition Amplitude of a Forced Harmonic Oscillator Charged Particle Interaction with Phonons : Path Integral Perturbation Theory Time-Dependent Perturbation Transition Probability Time-Energy Uncertainty Relation Density of Final State Transition Rate Continuous Spectrum due to a Constant Perturbation Harmonic Perturbation : Transition Matrix Element : Functional Derivative Functional Derivative of the Action Functional Functional Derivative and Matrix Element : Quantum Statistical Mechanics Functional Integral Approach Introduction Density Matrix Partition Function Expectation Value of a Physical Observable Density Matrix Density Matrix in the Energy Representation : Partition Function and Density Matrix Path Integral Representation Density Matrix Path Integral Representation Density Matrix Operator Average Value in Phase Space Generalized Gaussian Functional Path Integral in Phase Space Density Matrix via Transition Amplitude Partition Function in the Path integral Representation Particle Interaction with a Driven or Forced Harmonic Oscillator: Partition Function Free Particle Density Matrix and Partition Function Quantum Harmonic Oscillator Density Matrix and Partition Function : Quasi-Classical Approximation in Quantum Statistical Mechanics Centroid Effective Potential Expectation Value : Feynman Variational Method : Polaron Theory Introduction Polaron Energy and Effective Mass Functional Influence Phase Polaron Model Lagrangian Polaron Partition Function Influence Phase via Feynman Functional Integral in The Density Matrix Representation Expectation Value of a Physical Quantity Density matrix Full System Polaron Partition Function in a 3D Structure Model System Polaron Partition Function in a 3D Structure Feynman Inequality and Generating Functional Polaron Characteristics in a 3D Structure Polaron Asymptotic Characteristics Polaron Characteristics in a Quasi-1D Quantum Wire Hamiltonian of the Electron in a Quasi 1D Quantum Wire Lagrangian of the Electron in a Quasi-1D Quantum Wire Partition function of the Electron in a Quasi-1D Quantum Wire Polaron Generating Function Polaron Asymptotic Characteristics Strong Coupling Regime Polaron Characteristics Bipolaron Characteristics in a Quasi-1D Quantum Wire Introduction Bipolaron Diagrammatic Representation Bipolaron Lagrangian Bipolaron Equation of Motion Transformation into Normal Coordinates Diagonalization of the Lagrangian Bipolaron Partition Function Bipolaron Generating Function Bipolaron Asymptotic Characteristics Polaron Characteristics in a Quasi-0D Spherical Quantum Dot Introduction Polaron Lagrangian Normal Modes Lagrangian Diagonalization Transformation to Normal Coordinates Polaron Partition Function Generating Function Bipolaron Characteristics in a Quasi-0D Spherical Quantum Dot Introduction Model Lagrangian Model Lagrangian Equation of Motion and Normal Modes Diagonalization of the Lagrangian Partition Function Full System Influence Phase Bipolaron Energy Generating Function Bipolaron Characteristics Polaron Characteristics in a Cylindrical Quantum Dot System Hamiltonian Transformation to Normal Coordinates Lagrangian Diagonalization Polaron Energy/Partition Function Polaron Generating Function Polaron Energy Bipolaron Characteristics in a Cylindrical Quantum Dot System Hamiltonian Model System Action Functional Equation of Motion / Normal Modes Lagrangian Diagonalization Bipolaron Partition Function Bipolaron Generating Function Bipolaron Energy Polaron Characteristics in a Quasi-0D Cylindrical Quantum Dot with Asymmetrical Parabolic Potential Polaron Energy Bipolaron Characteristics in a Quasi-0D Cylindrical Quantum Dot with Asymmetrical Parabolic Potential Polaron in a Magnetic Field : Multiphoton Absorption by Polarons in a Spherical Quantum Dot Theory of Multiphoton Absorption by Polarons Basic Approximations Absorption Coefficient : Polaronic Kinetics in a Spherical Quantum Dot : Kinetic Theory of Gases Distribution Function Principle of Detailed Equilibrium Transport Phenomenon and Boltzmann-Lorentz Kinetic Equation Transport Relaxation Time Boltzmann H-Theorem Thermal Conductivity Diffusion