Computational physics is a good way to get valuable intuition about the key equations of physics, and train your numerical analysis skills:
- classical mechanics
- "Real-time heat equation OpenGL visualization with interactive mouse cursor using relaxation method" under the best articles by Ciro Articles
- phet.colorado.edu PhET simulations from University of Colorado Boulder
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Ah, the jewel of computational physics.
Also known as an ab initio method: no experimental measurement is taken as input, QED is all you need.
But since QED is thought to fully describe all relevant aspects molecules, it could be called "the" ab initio method.
For one, if we were able to predict protein molecule interactions, our understanding of molecular biology technologies would be solved.
No more ultra expensive and complicated X-ray crystallography or cryogenic electron microscopy.
And the fact that quantum computers are one of the most promising advances to this field, is also very very exciting: Section "Quantum algorithm".
- www.youtube.com/watch?v=NtnsHtYYKf0 "Mercury and Relativity - Periodic Table of Videos" by a
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Computational physics uses numerical algorithms to obtain and test predictions of physical models. It includes solving differential equations, simulating stochastic processes and extracting physical quantities from data. The mathematical model, its numerical approximation and its agreement with an experiment are separate questions: an accurately executed algorithm can still solve an unsuitable model.
A simple example is the harmonic oscillator . The explicit Euler method advances it byFor a unit mass, define . Direct substitution givesThe physical oscillator conserves energy, but this algorithm creates it on every step. The discrepancy is a numerical effect, not a discovery about the oscillator. Changing the time step and comparing with a known solution exposes the problem; for long integrations, the choice of numerical method matters as well as the size of the step.
Richard Feynman's lecture on planetary motion gives a concrete historical teaching example: forces determine accelerations, which update velocities and positions through successive arithmetic steps. A computer extends the same approach to systems whose coupled motion has no convenient closed expression.[ref]
The Feynman Lectures on Physics, Volume I by Richard Feynman and others. Chapter 9, section 9–7, Planetary motions, Table 9–2; www.feynmanlectures.caltech.edu/I_09.html
Conservation checks, comparison against solvable limits, and convergence under finer numerical resolution help distinguish a reliable calculation from an attractive plot. Agreement with measurements then tests the physical model itself.
Computational physics is a branch of physics that employs numerical methods and algorithms to solve complex physical problems that cannot be addressed analytically. It encompasses the use of computational techniques to simulate physical systems, model phenomena, and analyze data, thereby facilitating a deeper understanding of physical processes. Key aspects of computational physics include: 1. **Methodology**: This involves the development and implementation of algorithms to solve equations that arise from physical theories.