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The discovery that waves could be measured in particle-like packets of energy called quanta led to this branch of physics, which deals with atomic and subatomic systems.

quantum mechanics incorporates four classes of phenomena that classical physics cannot account for:

  1. The quantization (discretization) of certain physical quantities
  2. Wave-particle duality
  3. The uncertainty principle - Heisenberg's Uncertainty Principle which states that there is an uncertainty in position of any subatomic particle including the electron so to describe where an electron or other particle is, the entire range of possible values is used describing a probability distribution. It could be anywhere the particle's wave packet has non-zero amplitude.

    It is more commonly stated as: "Certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. That is, the more precisely one property is known, the less precisely the other can be known.

  4. Quantum entanglement.

In the late 1920s, von Neumann developed the separable Hilbert space formulation of quantum mechanics, which later became the definitive one (from the standpoint of mathematical rigor, at least)

Matrix mechanics and wave mechanics were formulated roughly around the same time between 1925 and 1926. In July 1925, Heisenberg finished his seminal paper "On a Quantum Theoretical Interpretation of Kinematical and Mechanical Relations". Two months later, Born and Jordan finished their paper, "On Quantum Mechanics", which is the first rigorous formulation of matrix mechanics. Two months after this, Born, Heisenberg, and Jordan finished "On Quantum Mechanics II", which is an elaboration of the earlier Born and Jordan paper; it was published in early 1926. These three papers are reprinted in (van der Waerden 1967). Meanwhile, Schroedinger was working on what eventually became his four famous papers on wave mechanics. The first was received by Annalen der Physik in January 1926, the second one month later, and then the third in May and the fourth in June. All four are reprinted in (Schroedinger 1928).

Einstein was one of the founders of quantum mechanics, yet he disliked the randomness that lies at the heart of the theory. God does not, he famously said, play dice. However, quantum theory has survived a century of experimental tests, although it has yet to be reconciled with another of Einstein's great discoveries - the general theory of relativity.

Stuff to expand on - understand<BR> In Copenhagen in 1927 Heisenberg developed his uncertainty principle,[65] which Bohr embraced. In a paper he presented at the Volta Conference at Como in September 1927, he demonstrated that the uncertainty principle could be derived from classical arguments, without quantum terminology or matrices.[65] Einstein preferred the determinism of classical physics over the probabilistic new quantum physics to which he himself had contributed. Philosophical issues that arose from the novel aspects of quantum mechanics became widely celebrated subjects of discussion. Einstein and Bohr had good-natured arguments over such issues throughout their lives.
Einstein's famous quote " "God does not play dice with the universe." may be related to this uncertainty principle.
Einstein's 'God does not play dice' saying is misunderstood - Business Insider

It's true that Einstein never accepted quantum mechanics, but the reason was much more nuanced than a flat-out rejection of the theory. After all, Einstein won a Nobel Prize in 1921 for describing the photoelectric effect — a phenomenon that led to the development of quantum mechanics.

Quantum entanglement

last updated 26 Dec 2005