Comprehensive high-yield formula reference covering all 8 syllabus sections for GATE Physics (PH).
Schrödinger Eq = -(hbar²/2m) ∇²ψ + Vψ = ihbar ∂ψ/∂t
Harmonic Oscillator = E_n = (n + 1/2)hbaromega
Commutator = [x, p] = ihbar
Euler-Lagrange = (d/dt)(∂L/∂q̇_i) - ∂L/∂q_i = 0
Hamiltonian = H = ∑ p_i q̇_i - L
Poisson Brackets = {u, v} = ∑ (∂u/∂q_i ∂v/∂p_i - ∂u/∂p_i ∂v/∂q_i)
Maxwell Equations = ∇·E = ρ/ε₀ | ∇×B = μ₀J + μ₀ε₀ ∂E/∂t
Poynting Vector = S = (1/μ₀)(E × B)
Wave Velocity = v = 1/√(με)
Partition Function = Z = ∑ g_i exp(-β E_i)
Helmholtz Free Energy = F = -k_B T ln Z
Quantum Distributions = n_FD = 1/(e^(β(E-μ)) + 1) | n_BE = 1/(e^(β(E-μ)) - 1)
Bragg's Law = 2d sin θ = nλ
Fermi Energy = E_F = (hbar²/2m) (3π² n)^(2/3)
Effective Mass = m* = hbar² / (d²E/dk²)
Bohr Radius = a₀ = 4πε₀ hbar² / (m e²)
Landé g-factor = g = 1 + [J(J+1) + S(S+1) - L(L+1)] / [2J(J+1)]
Zeeman Splitting = ΔE = g μ_B B m_j
Newton-Raphson = x_{n+1} = x_n - f(x_n) / f'(x_n)
Simpson's 1/3 Rule = ∫y dx = (h/3) [y0 + 4∑y_odd + 2∑y_even + yn]
Eigenvalues = det(A - λI) = 0
Relative Speed = S1 + S2 (Opposite) | S1 - S2 (Same)
Combined Work Rate = 1/T = 1/T1 + 1/T2
Combinations = nCr = n! / [r! (n - r)!]
Practice Questions Using These Formulas