Nonlinear Spectroscopy: Quantum Effects

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Covers the storage of flow field data, differential operators, equivariance vs invariance, and symmetries in ChannelFlow.

Covers the concept of general transformations in quantum mechanics.

Covers the Maxwell field, symmetries, and making shifts in local and covariant derivatives.

Introduces the concept of discrete symmetries in Quantum Field Theory and their impact on particles and anti-particles.

Explores center of mass calculation in mechanics, emphasizing system symmetry and spherical coordinates for simplifying calculations.

Explores the classification and practical applications of symmetries in 3D space, emphasizing user-driven determination of object symmetries.

Introduces group representations theory in quantum physics, covering symmetries, perturbation theory, and energy state degeneracy.

Explores fundamental theorems and practical applications of modern symmetry theory, including decorative motifs and linear pattern extensions.

Explores symmetries in diffusion equations, showing how they simplify analysis and infer solution properties.

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.