Yukawa had originally named his particle the " mesotron ", but he was corrected by the physicist Werner Heisenberg ( whose father was a professor of Greek at the University of Munich ).

Bohr and Heisenberg extended the probabilistic interpretation of the wavefunction proposed originally by Max Born.

Heisenberg explained this as a disturbance caused by measurement.

Tunnelling is often explained using the Heisenberg uncertainty principle and the wave – particle duality of matter.

A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at the same time ; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926.

In the following years, with contributions from Wolfgang Pauli, Eugene Wigner, Pascual Jordan, Werner Heisenberg and an elegant formulation of quantum electrodynamics due to Enrico Fermi, physicists came to believe that, in principle, it would be possible to perform any computation for any physical process involving photons and charged particles.

This makes them all radical libertarians, as opposed to those who limit chance to the early deliberative stages of the decision process, such as James, Popper, Margenau, Doyle and Martin Heisenberg, who are conservative or modest libertarians, following the two-stage models proposed by Dennett and Mele.

There, apart from the Heisenberg, or Schrödinger ( position or momentum ), or phase-space representations, one also encounters the Fock ( number ) representation and the Segal – Bargmann ( Fock-space or coherent state ) representation ( named after Irving Segal and Valentine Bargmann ).

Since the Heisenberg principle limits the precision of any measurement of the combination of an electron's momentum ( related to energy ) and its position, in a crystal effectively the available energy levels form a continuous band of allowed energy levels.

The spatial spread of the wave packet, and the spread of the wavenumbers of sinusoids that make up the packet, correspond to the uncertainties in the particle's position and momentum, the product of which is bounded by Heisenberg uncertainty principle.

For example, the Heisenberg uncertainty principle states that one cannot simultaneously know, with arbitrarily high precision, both the position and momentum of a particle.

Because of the zero-point energy, the position and momentum of the oscillator in the ground state are not fixed ( as they would be in a classical oscillator ), but have a small range of variance, in accordance with the Heisenberg uncertainty principle.

Using the Heisenberg uncertainty principle for position and momentum, the products of uncertainty in position and momentum become zero as ħ → 0:

In quantum mechanics, the Heisenberg Uncertainty Principle puts limits on how much an observer can ever know about the position and velocity of a particle.

Therefore, since ( according to the Heisenberg uncertainty principle ) < span style =" white-space: nowrap "> ΔpΔx ≥ ħ / 2 </ span > where Δp is the uncertainty in the particle's momentum and Δx is the uncertainty in position, then we must say that their momentum is extremely uncertain since the particles are located in a very confined space.

This trade-off between spread in position and spread in momentum is one example of the Heisenberg uncertainty principle.

One interpretation of this duality involves the Heisenberg uncertainty principle, which defines a limit on how precisely the position and the momentum of a particle can be known at the same time.

Informally stated, with certain technical assumptions, every representation of the Heisenberg group is equivalent to the position operators and momentum operators on R < sup > n </ sup >.

Josef Segman proposed the idea of incorporating scale into the Heisenberg group ( position, momentum, phase, or equivalently any canonical conjugate variables taken together with phase, such as, for example, time, frequency, and phase ).

The position and momentum in this phase space are mapped to the generators of the Heisenberg group, and the Hilbert space appears as a group representation of the Heisenberg group.

More specifically, due to the Heisenberg uncertainty principle, an electron in a crystal cannot have both an exactly-defined k and an exact position in the crystal.

The only difference is that the Heisenberg ’ s uncertainty principle musn ’ t be violated, meaning that we cannot measure the particle ’ s momentum and position at the same time.

The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once.

According to an apocryphal story, Werner Heisenberg was asked what he would ask God, given the opportunity.

A later conference would include Niels Bohr, Werner Heisenberg, Max Born, and Erwin Schrödinger.

Due to the problematic divergences present in quantum field theory at that time Heisenberg was motivated to isolate the essential features of the theory that would not be affected by future changes as the theory developed.

Heisenberg would later employ his " Jewish physics ," in the German project to develop nuclear fission for the purposes of nuclear weapons or nuclear energy use.

Himmler promised Heisenberg that after Germany won the war, the SS would finance a physics institute to be directed by Heisenberg.

If, of course, it were possible to predict the change in the parameters, then there would be other parameters which were unchanged, but the search for ultimately stable parameters in evolutionary systems is futile, for they probably do not exist .... Social systems have Heisenberg principles all over the place, for we cannot predict the future without changing it.

Therefore, in the Heisenberg picture, if the classical information is part of, say, the input, we would define to include the relevant classical observables.

Heisenberg was impressed by Heim's knowledge, but thought the approach would be impractical.

Bohr had concluded that they would have both drowned had he jumped in to save his son, and this presents an idea of futile heroics, particularly with reference to Heisenberg and what should happen if he were to resist Hitler ’ s rule.

Up until that time, attempts to make the old quantum theory of the atom compatible with the theory of relativity, attempts based on discretizing the angular momentum stored in the electron's possibly non-circular orbit of the atomic nucleus, had failed-and the new quantum mechanics of Heisenberg, Pauli, Jordan, Schrödinger, and Dirac himself had not developed sufficiently to treat this problem.

Sufficiently dense matter containing protons experiences proton degeneracy pressure, in a manner similar to the electron degeneracy pressure in electron-degenerate matter: protons confined to a sufficiently small volume have a large uncertainty in their momentum due to the Heisenberg uncertainty principle.

Similar interdependencies between two particular measurements and the corresponding operators are the uncertainty relations as first expressed by Heisenberg for the interdependence between measurements of distance and of momentum, and as generalized by Edward Condon, Howard Percy Robertson, and Erwin Schrödinger.

The Heisenberg Uncertainty Principle states that exact measurements of positions and momentum cannot be known, together, with more than a given precision.

On the other hand according to the Heisenberg uncertainty principle, a measurement of a space-time separation causes an uncertainty in momentum inversely proportional to the extent of the separation.

The Heisenberg picture is the closest to classical Hamiltonian mechanics ( for example, the commutators appearing in the above equations directly translate into the classical Poisson brackets ); but this is already rather " high-browed ", and the Schrödinger picture is considered easiest to visualize and understand by most people, to judge from pedagogical accounts of quantum mechanics.

The Heisenberg uncertainty principle is a famous example of the uncertainty in quantum mechanics.

" Physicists attempt to reduce the complexity of nature to a single unifying theory, of which the most successful and universal, the quantum theory, has been associated with several Nobel prizes, for example those to Dirac and Heisenberg.

* An example: dmrg of Heisenberg model

Concretely, by a central representation one means a representation such that the center of the Heisenberg group maps into the center of the algebra: for example, if one is studying matrix representations or representations by operators on a Hilbert space, then the center of the matrix algebra or the operator algebra is the scalar matrices.

A closely related example of a sub-Riemannian metric can be constructed on a Heisenberg group: Take two elements and in the corresponding Lie algebra such that

For example, the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics should be built in.

As an example, let G be the discrete Heisenberg group.

( In example, Heisenberg refers to a “ bomb having gone off ” in Bohr ’ s head.

For example, in a 1998 book, Heisenberg and the Nazi atomic bomb project: a study in German culture Paul Lawrence Rose had speculated that Heisenberg had visited Bohr as " an intelligence-gathering mission.

Michael Frayn's Tony Award-winning Copenhagen ( 1998 ), for example, contemplates the ethics and early history of nuclear weapons development through the eyes of the physicist Niels Bohr, his wife Margarethe, and his former pupil Werner Heisenberg.

Another elementary 3-parameter example is given by the Heisenberg group and its Lie algebra.

( For example, Nobel Prize winner Philipp Lenard claimed scientific thought was conditioned by " blood and race ", and he accused Werner Heisenberg of teaching " Jewish physics ".