09-20-2021-0859 - Matrix Mechanics

Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation.

In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operatormethods.^[1] Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926,^[2] before the development of wave mechanics.

https://en.wikipedia.org/wiki/Matrix_mechanics 

The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.

https://en.wikipedia.org/wiki/Path_integral_formulation

https://en.wikipedia.org/wiki/Bra–ket_notation

https://en.wikipedia.org/wiki/Antilinear_map

https://en.wikipedia.org/wiki/linear_map

https://en.wikipedia.org/wiki/Paul_Dirac

https://en.wikipedia.org/wiki/J._Robert_Oppenheimer

https://en.wikipedia.org/wiki/George_Gamow

https://en.wikipedia.org/wiki/Richard_Feynman

https://en.wikipedia.org/wiki/Wolfgang_Pauli

https://en.wikipedia.org/wiki/Mathematical_beauty

https://en.wikipedia.org/wiki/Ladder_operator

https://en.wikipedia.org/wiki/Matrix_mechanics

https://en.wikipedia.org/wiki/Dirac_delta_function

https://en.wikipedia.org/wiki/Poisson_bracket

https://en.wikipedia.org/wiki/Renormalization

https://en.wikipedia.org/wiki/Pion

https://en.wikipedia.org/wiki/Scalar_field

https://en.wikipedia.org/wiki/Pseudoscalar_meson

https://en.wikipedia.org/wiki/Interaction_picture#Schwinger-Tomonaga_equation

https://en.wikipedia.org/wiki/Atomic_electron_transition