Quantum mechanics

The most advanced and toughest subject related to physics, especially mechanics is the quantum mechanics.it actually starts with the the famous scientist's works "Schrodinger's equation" and "Heisenberg picture". But the basics are derived from max planc's quantum theory. Let us see about it in detail.

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of the wave–particle duality of matter and energy. The theory was developed in 1925 by Werner Heisenberg. Quantum mechanics describes the time evolution of physical systems via a mathematical structure called the wave function. The wave function encapsulates the probability that the system is to be found in a given state at a given time. Quantum mechanics also allows one to calculate the effect on the system of making measurements of properties of the system by defining the effect of those measurements on the wave function. This leads to the well-known uncertainty principle as well as the enduring debate over the role of the experimenter, epitomised in the Schrödinger's Cat thought experiment.

Quantum mechanics differs significantly from classical mechanics in its predictions when the scale of observations becomes comparable to the atomic and sub-atomic scale, the so-called quantum realm. However, many macroscopic properties of systems can only be fully understood and explained with the use of quantum mechanics. Phenomena such as superconductivity, the properties of materials such as semiconductors and nuclear and chemical reaction mechanisms observed as macroscopic behaviour, cannot be explained using classical mechanics.

The term was coined by Max Planck, and derives from the observation that some physical quantities can be changed only by discrete amounts, or quanta, as multiples of the Planck constant, rather than being capable of varying continuously or by any arbitrary amount. For example, the angular momentum, or more generally the action, of an electron bound into an atom or molecule is quantized. Although an unbound electron does not exhibit quantized energy levels, one which is bound in an atomic orbital has quantized values of angular momentum. In the context of quantum mechanics, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons and other atomic-scale objects.

The mathematical formulations of quantum mechanics are abstract. Similarly, the implications are often counter-intuitive in terms of classical physics. The centerpiece of the mathematical formulation is the wavefunction (defined by Schrödinger's wave equation), which describes the probability amplitude of the position and momentum of a particle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. The wavefunction treats the object as a quantum harmonic oscillator and the mathematics is akin to that of acoustic resonance.