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 operator methods.[1] Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926,[2] before the development of wave mechanics.
^Herbert S. Green (1965). Matrix mechanics (P. Noordhoff Ltd, Groningen, Netherlands) ASIN : B0006BMIP8.
^Pauli, W (1926). "Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik". Zeitschrift für Physik. 36 (5): 336–363. Bibcode:1926ZPhy...36..336P. doi:10.1007/BF01450175. S2CID 128132824.
Matrixmechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually...
laid the groundwork for matrixmechanics that would come to substitute old quantum theory, leading to the modern quantum mechanics. Heisenberg received the...
invented his matrixmechanics, which was the first correct quantum mechanics–– the essential breakthrough. Heisenberg's matrixmechanics formulation was...
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation...
Max Born and Pascual Jordan, during the same year, his matrix formulation of quantum mechanics was substantially elaborated. He is known for the uncertainty...
modern quantum mechanics was born in 1925, when the German physicists Werner Heisenberg, Max Born, and Pascual Jordan developed matrixmechanics and the Austrian...
the probability of finding a particle at a given point in space. The matrixmechanics of Werner Heisenberg (1925) makes no mention of wave functions or similar...
the identity matrix. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted...
Matrixmechanics is an alternative formulation that allows considering systems with a finite-dimensional state space. Quantum statistical mechanics generalizes...
two earliest formulations of quantum mechanics – matrixmechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger). An...
In 1925 Born and Werner Heisenberg formulated the matrixmechanics representation of quantum mechanics. The following year, he formulated the now-standard...
quantum mechanics represents observable quantities like the energy. For a particle that has equal amplitude to move left and right, the Hermitian matrix H is...
contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matrixmechanics, and developed canonical...
interpretation of quantum mechanics The definition of quantum theorists' terms, such as wave function and matrixmechanics, progressed through many stages...
principle. The wave mechanics picture of the uncertainty principle is more visually intuitive, but the more abstract matrixmechanics picture formulates...
ISBN 0061305499. LCCN 99010404. Lakshmibala, S. (2004). "Heisenberg, MatrixMechanics and the Uncertainty Principle". Resonance: Journal of Science Education...
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element...
passive transformations. The Heisenberg picture is the formulation of matrixmechanics in an arbitrary basis, in which the Hamiltonian is not necessarily...
the notion in quantum mechanics, see scattering matrix. In multivariate statistics and probability theory, the scatter matrix is a statistic that is...
momentum variables of the equations of classical mechanics. They applied the rules of matrixmechanics to a few highly idealized problems and the results...
n} matrices. In some fields, such as group theory or quantum mechanics, the identity matrix is sometimes denoted by a boldface one, 1 {\displaystyle \mathbf...
ambiguities and inconsistencies. Schrödinger's wave mechanics developed separately from matrixmechanics until Schrödinger and others proved that the two...
Historically, around 1926, Schrödinger and Heisenberg show that wave mechanics and matrixmechanics are equivalent, later furthered by Dirac using transformation...
transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing...
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