Quantum mechanics

Quantum mechanics

• Quantum mechanics (QM – also known as quantum physics or quantum theory) is a branch of physics which deals with physical phenomena at microscopic scales, where the action is on the order of the Planck constant. Quantum mechanics departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. Quantum mechanics is the non-relativistic limit of Quantum Field Theory (QFT), a theory that was developed later that combined Quantum Mechanics with Relativity.

Schrödinger  Q.M

• Erwin Rudolf Josef Alexander Schrödinger 

12 August 1887 – 4 January 1961), was an Austrian physicist who developed a number of fundamental results in the field of quantum theory, which formed the basis of wave mechanics: he formulated the wave equation (stationary and time-dependent Schrödinger equation) and revealed the identity of his development of the formalism and matrix mechanics. • Matrix mechanics is a formulation of quantum

mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925

• It is equivalent to the Schrödinger wave formulation of quantum mechanics, and is the basis of Dirac's bra-ket notation for the wave function.

•  Schrödinger equation• In quantum mechanics, the Schrödinger equation is a partial differential

equation that describes how the quantum state of some physical system changes with time. It was formulated in late 1925

Time-dependent Schrödinger equation (general)

Time-independent Schrödinger equation (general)

Erwin Rudolf Josef Alexander Schrödinger (12 August 1887 – 4 January 1961)

• Schrödinger proposed an original interpretation of the physical meaning of the wave function and in subsequent years repeatedly criticized the conventional Copenhagen interpretation of quantum mechanics (using e.g. the paradox of Schrödinger's cat). In addition, he was the author of many works in various fields of physics: statistical mechanics and thermodynamics, physics of dielectrics, color theory, electro dynamics, general relativity, and cosmology, and he made several attempts to construct a unified field theory.

• In his book What Is Life? Schrödinger addressed the problems of genetics, looking at the phenomenon of life from the point of view of physics. He paid great attention to the philosophical aspects of science, ancient and oriental philosophical concepts, ethics and religion. He also wrote on philosophy and theoretical biology

Hamiltonian mechanics

• Sir William Rowan Hamilton (midnight, 3-4 August 1805 – 2 September 1865) was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. His greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In mathematics, he is perhaps best known as the inventor of quaternions.

William Rowan Hamilton

(August 1805 – 2 September 1865)

The time evolution of the system is uniquely defined by Hamilton's equations

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