Computational Physics

 

Computational Physics:

Introduction:

The study and application of numerical analysis to physics problems for which a quantitative theory already exists is known as computational physics. Computational physics, a branch of computational science, was historically the first field of research to use modern computers. It is sometimes viewed as a branch (or subdiscipline) of theoretical physics, although some people think of it as a research field that complements both theory and experiment.

 

Computational Physics

The difficulties of computational physics:

Problems in computational physics are notoriously challenging to address precisely. This is owing to a number of (mathematical) factors, including complexity, chaos, and a lack of algebraic and/or analytic solvability. For instance, it may take a lot of work to develop a workable algorithm (if one can be found), and other cruder or brute-force techniques, like graphical methods or root finding, may be necessary to solve even seemingly simple problems, like calculating the wavefunction of an electron orbiting an atom in a strong electric field (Stark effect). The more sophisticated mathematical perturbation theory is also occasionally employed (a working is shown for this particular example here).Additionally, many-body problems (and their classical counterparts) tend to have rising computing costs and complexity. It is rather problematic because the size of a macroscopic system's constituent particles is often on the scale of "displaystyle 10231023". For traditional N-body problems, the solution is of order N-squared and is typically of exponential order in the size of the system. Finally, it might be challenging to ensure that any numerical inaccuracies do not accumulate to the point that the "solution" is rendered meaningless because many physical systems are, at best, intrinsically nonlinear and, at worst, chaotic.

 

Applications:

Due to the wide range of issues it addresses, computational physics is a crucial part of current physics research in a number of fields, including: astrophysics, fluid mechanics (computational fluid dynamics), lattice field theory/lattice gauge theory (especially lattice quantum chromodynamics), plasma physics (see plasma modelling), and simulating physical systems (using, for example, molecular dynamics).

 

Computational Physics

Density functional theory, for instance, is utilised in computational solid state physics to compute solid properties in a manner akin to how chemists examine molecules. This method, as well as others, such as the Luttinger-Kohn/k.p method and ab-initio methods, can be used to compute other quantities of relevance in solid state physics, such as the electronic band structure, magnetic characteristics, and charge densities.