Gaussian Path Integrals: Properties and Composition

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Covers the path integral representation of the propagator and Gaussian integrals in complex and multi-dimensional cases.

Path Integral Representation of Propagators

Covers the path integral representation of propagators for free particles and harmonic oscillators.

Gaussian Path Integrals: Composition Property

Explores wave packet evolution, path integrals, and Gaussian composition properties in quantum mechanics.

Gelfand-Yaglom Formula

Explores the Gelfand-Yaglom formula and time-ordered products in the context of the path integral representation of the propagator for a time-dependent harmonic oscillator.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Position Space Approach: Analyzing Banana Feynman Diagrams

Presents the position space approach to banana Feynman diagrams and their differential equations.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Homogeneous Differential Equations

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.