Mathematical & Computational Physics
4 terms
Hamiltonian Formalism
Mathematical & Computational Physics
Joules (Energy)
A formulation of classical mechanics describing system dynamics in 2N-dimensional phase space using position q_i and canonical momentum p_i.
H(q, p, t) = ∑ p_i q̇_i - L, q̇_i = ∂H / ∂p_i, ṗ_i = -∂H / ∂q_i
Hermite Polynomials
Mathematical & Computational Physics
Dimensionless Orthogonal Polynomials
A sequence of classical orthogonal polynomials satisfying Hermite's differential equation y'' - 2x y' + 2n y = 0.
H_n(x) = (-1)^n e^(x²) (d^n / dx^n) (e^(-x²))
Hessian Matrix
Mathematical & Computational Physics
Second Derivative Matrix
A square matrix of second-order partial derivatives of a scalar-valued function, describing local surface curvature and local extrema stability.
H_ij = ∂²f / (∂x_i ∂x_j)
Hilbert Space
Mathematical & Computational Physics
Complete Inner Product Space
A complete abstract vector space possessing an inner product that allows length and angle to be defined for infinite-dimensional function spaces.
⟨f, g⟩ = ∫ f*(x) g(x) dx, ||f|| = √(⟨f, f⟩)