Computational Physics Guide

Computational Physics Guide

Apply computational methods to physics research, including molecular dynamics, Monte Carlo simulations, quantum computing, and numerical methods for solving physical systems.

Computational Methods Overview

Molecular Dynamics

Basic MD Algorithm

import numpy as np

def lennard_jones(r, epsilon=1.0, sigma=1.0):
    """Lennard-Jones potential and force."""
    r6 = (sigma / r) ** 6
    r12 = r6 ** 2
    potential = 4 * epsilon * (r12 - r6)
    force = 24 * epsilon * (2 * r12 - r6) / r
    return potential, force

def velocity_verlet(positions, velocities, forces, masses, dt):
    """Velocity Verlet integration step."""
    # Half-step velocity update
    velocities += 0.5 * forces / masses * dt
    # Full-step position update
    positions += velocities * dt
    # Compute new forces
    new_forces = compute_forces(positions)
    # Complete velocity update