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# Mathematical Physics

Physics and maths have undergone an intensely symbiotic period over the last two decades and are poised to even more exciting and productive relationship into the twenty-first century. The mathematical physics is nothing but using the maths methods systematically for solving the physics problems and applying it for the physics concepts. There are various topics in mathematical physics like tensors, algebraic structures, matrices and dual spaces, eigenvalue problems, Riemann theorem, spherical harmonics, adjoint and unitary transformations etc. It is quite vast topic with various branches, topics etc. Lets see more about it.

## Branches of Mathematical Physics

Mathematical physics is an interdisciplinary branch of physics where the theoretical physics and mathematics concepts get related to solve out the concepts related to quantum mechanics, classical theory, relativistic theory etc and gives a new physical theory. There are several branches in mathematical physics namely
1. Classical Mechanics
2. Partial Differential Equations
3. Quantum Theory
4. Relativity and Quantum Relativistic Theories
5. Statistical Mechanics

These branches were developed in the second half of eighteenth century almost in 1930's which rather contains different type of mathematical methods which proves some physics concepts.

## Partial Differential Equations

A partial differential equation is the equation  which consists of two or more independent variables with a unknown function and a quantity having a partial derivatives with respect to independent variables. The order of a partial differential equation has the highest order derivative. It formulates the solution giving out the understanding about velocity, heat, sound propagation, elasticity, flow of fluid, electrostatics, electrodynamics etc. There are first order, second order up to nth order derivatives in partial derivatives that gives the solution to any number of quantities.

## Quantum Theory

It is the theoretical physics that explains the nature and behavior of matter and energy on the atomic and sub atomic particles. The interpretation of this theory came out in twentieth century by Bohr and Heisenberg in 1927. It explains in solids at most basic level why some solids are metals, some are insulators and others are semiconductors. It consists of various concepts like wave particle duality, wave quantization, Heisenberg uncertainty principle, Schrodinger's equation, expectation value and momentum operator, variational principle, energy in finite square well and infinite square well etc.

## Classical Mechanics

Mechanics is the study of how things move. The term classical mechanics is something really vague but gives the equivalent formulations of mechanics. Until the beginning of twentieth century, it seemed that classical mechanics to be the only kind of mechanics that described the possible motion. Then, in the twenty years from 1905 to 1925, it became very clear that classical mechanics did not correctly describe the motion of objects moving at speeds close to the speed of light, nor that of microscopic particles inside atoms and molecules. The result was development of two forms of mechanics namely the relativistic mechanics that described the high speed motions and quantum mechanics that described the motion of microscopic particles.

## Statistical Mechanics

Matter consists of atoms which are distributed in the system. The statistical physics starts from the microscopic level which discusses not only thermal-equilibrium states, but also non equilibrium states. It aims at understanding the properties of liquids, solids or gases on the basis of laws of motion of atoms and molecules.Statistical mechanics is a branch of physics  that deals with the study of thermodynamic behavior of the systems containing large number of particles, free energy of the system etc. It consists of ergodic theory and many parts of probability theory.