Home > Computational physics

Physicists often have a very precise mathematical theory describing how a system will behave. Unfortunately, it is often the case that solving the theory's equations in order to produce a useful prediction is a computationally difficult problem. This is especially true with quantum mechanics, where only a handful of simple models can be solved exactly. Even apparently simple problems, such as calculating the wavefunction of an electron orbiting an atom in a strong electric field, may require great effort to formulate a practical algorithm.

In addition, the computational cost of solving quantum mechanical problems is generally exponential in the size of the system (see computational complexity theory).

Many other more general numerical problems fall loosely under the domain of computational physics, although they could easily be considered pure mathematics or part of any number of applied areas. For example:

• Solving differential equations
• Evaluating integrals
• Stochastic methods, specifically the Monte Carlo Method
• Specialised partial differential equation methods, for example the finite difference method and the finite element method
• The matrix eigenvalue problem – i.e. the problem of finding eigenvalueIn linear algebra, a scalar λ is called an eigenvalue (in some older texts, a characteristic value of a linear mapping A if there exists a nonzero vector x such that Ax &lambda x''. The vector x is called an eigenvector. In matrix theory, an elemens of very large matrices.
• The pseudo-spectral methodThe pseudo-spectral method is a method in computational physics used for direct simulation of a particle with an arbitrary wavefunction interacting with an arbitrary potential. Background The Schrodinger wave equation, : can be written : which bears remar

See also important publications in computational physicsClassical mechanics Philosophiae Naturalis Principia Mathematica Isaac Newton Description The Philosophiae Naturalis Principia Mathematica ( Latin: "mathematical principles of natural philosophy", often Principia or Principia Mathematica for short) is a t