the basics and the introduction to the schrodinger and hamiltanion equations are explained here

2. 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.

3. 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.

4. • 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)

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

6. • 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

7. 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.

8. William Rowan Hamilton
(August 1805 – 2 September 1865)

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

10. • Quantum Computing
• Quantum Cryptography
• Quantum Teleportation
• Elitzur–Vaidman Bomb-Tester