physics-solver

name physics-solver description Physics problem solving including classical mechanics, electromagnetism, thermodynamics, quantum mechanics, optics, and computational physics. Use when user asks to solve physics problems, simulate physical systems, derive equations, or do unit conversions. Triggers on "physics problem", "Newton's law", "electromagnetic", "quantum", "thermodynamics", "optics", "wave equation", "Schrödinger", "relativity", "unit conversion", "circuit analysis". Physics Solver Physics computation and problem solving. Venv: source /Users/zhangmingda/clawd/.venv/bin/activate Physical Constants from scipy import constants as const import numpy as np # Key constants c = const.c # speed of light (m/s) h = const.h # Planck's constant (J·s) hbar = const.hbar # reduced Planck's constant k_B = const.k # Boltzmann constant (J/K) e = const.e # elementary charge (C) m_e = const.m_e # electron mass (kg) m_p = const.m_p # proton mass (kg) G = const.G # gravitational constant N_A = const.N_A # Avogadro's number epsilon_0 = const.epsilon_0 # vacuum permittivity mu_0 = const.mu_0 # vacuum permeability sigma = const.sigma # Stefan-Boltzmann constant Classical Mechanics from sympy import * t = symbols( 't' ) m, g, k, L = symbols( 'm g k L' , positive= True ) # Lagrangian mechanics # Example: Simple pendulum theta = Function( 'theta' )(t) T = Rational( 1 , 2 ) * m * (L * diff(theta, t))** 2 # kinetic energy V = -m * g * L * cos(theta) # potential energy Lag = T - V # Euler-Lagrange equation EL = diff(diff(Lag, diff(theta, t)), t) - diff(Lag, theta) eq = simplify(EL) print ( f"Equation of motion: {eq} = 0" ) # Numerical simulation (projectile, pendulum, etc.) from scipy.integrate import solve_ivp def pendulum ( t, state, g= 9.81 , L= 1.0 ): theta, omega = state return [omega, -g/L * np.sin(theta)] sol = solve_ivp(pendulum, [ 0 , 10 ], [np.pi/ 4 , 0 ], max_step= 0.01 ) Electromagnetism # Coulomb's law def coulomb_force ( q1, q2, r ): """Force between two charges (N)""" return const.k * q1 * q2 / r** 2 # k = 1/(4πε₀) # Capacitor energy def capacitor_energy ( C, V ): return 0.5 * C * V** 2 # RC circuit def rc_discharge ( V0, R, C, t ): tau = R * C return V0 * np.exp(-t / tau) # Electromagnetic wave def em_wavelength ( frequency ): return const.c / frequency def photon_energy ( wavelength ): return const.h * const.c / wavelength Quantum Mechanics # Particle in a box energy levels def particle_in_box ( n, L, m=const.m_e ): """Energy of nth level, box length L""" return (n** 2 * const.h** 2 ) / ( 8 * m * L** 2 ) # Hydrogen atom energy levels def hydrogen_energy ( n ): """Energy in eV""" return - 13.6 / n** 2 # de Broglie wavelength def de_broglie ( p ): return const.h / p # Heisenberg uncertainty # Δx · Δp ≥ ℏ/2 Thermodynamics & Statistical Mechanics # Ideal gas def ideal_gas_pressure ( n, T, V ): return n * const.R * T / V # Carnot efficiency def carnot_efficiency ( T_hot, T_cold ): return 1 - T_cold / T_hot # Blackbody radiation (Planck's law) def planck_spectral_radiance ( wavelength, T ): """W/(m²·sr·m)""" return ( 2 * const.h * const.c** 2 / wavelength** 5 ) / \ (np.exp(const.h * const.c / (wavelength * const.k * T)) - 1 ) # Maxwell-Boltzmann speed distribution def mb_speed_dist ( v, T, m ): return 4 * np.pi * (m / ( 2 * np.pi * const.k * T))** 1.5 * \ v** 2 * np.exp(-m * v** 2 / ( 2 * const.k * T)) Unit Conversion # scipy.constants has conversion factors from scipy.constants import eV, atm, calorie, mile, inch # Common conversions def eV_to_J ( energy_eV ): return energy_eV * eV def J_to_eV ( energy_J ): return energy_J / eV def celsius_to_kelvin ( T_C ): return T_C + 273.15 def atm_to_Pa ( P_atm ): return P_atm * atm Problem-Solving Framework Identify the physical system and relevant principles Draw a diagram (describe it textually) List knowns and unknowns Choose appropriate equations/laws Solve symbolically first (SymPy), then substitute numbers Check units, limiting cases, and order of magnitude Interpret the result physically Tips Always carry units through calculations Check dimensional consistency Verify with limiting cases (e.g., v << c for classical limit) Use SymPy for symbolic derivations, SciPy for numerical For complex simulations, consider specialized tools (COMSOL, OpenFOAM)