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...ld on a plane is described by the following four variables:<ref>Z.Ezawa. ''Quantum Hall Effect'', 2nd ed, World Scientific. Chapter 28</ref> guiding center co ...Q =q</math> and <math> P=-i\hbar \frac{d}{dq} </math> in one-dimensional [[quantum mechanics]]. ...

...[[Lagrangian mechanics#Quantum mechanics|Lagrangian]]s and [[Hamiltonian (quantum mechanics)|Hamiltonians]], which conventionally are both required to be [[H ...h in turn guarantees that the combined operator's eigenvalues will be real numbers, suitable for predicting values of observations / measurements.<ref name=Öz ...

...oning theorem]]), making it impossible to forge quantum money by including quantum systems in its design. ...uenced the development of [[quantum key distribution]] protocols used in [[quantum cryptography]]. ...

...complexity have led to the quantum version of the [[Cook–Levin theorem]]. Quantum Hamiltonian complexity has helped physicists understand the difficulty of s ...h>H</math>, and let <math>a</math> and <math>b</math> be non-negative real numbers with <math>b \geq a + 1</math>. If <math>\lambda_0 \leq a</math>, output Ye ...

In [[quantum chemistry]], the '''Dunham expansion''' is an expression for the rotational ...and [[Rigid rotor#Quantum mechanical linear rigid rotor|rotational quantum numbers]], and <math>\Omega</math> is the projection of <math>J</math> along the in ...

...envalue <math>q</math>.<ref>{{Cite book |last=Messiah |first=Albert |title=Quantum Mechanics |publisher=North-Holland |year=1961 |volume=I |location=Amsterdam Good quantum numbers are often used to label initial and final states in experiments. For exampl ...

{{Short description|Non-perturbative technique in quantum chromodynamics}} In [[quantum chromodynamics]], the [[color confinement|confining]] and strong coupling n ...

{{Short description|Number specifying how a quantum operator changes under dilations}} ...le invariance|scale invariant]], scaling dimensions of operators are fixed numbers, otherwise they are functions of the distance scale. ...

...CarleoTroyer:2016" /> to approximate [[wave functions]] of [[many-body]] [[quantum]] systems. ...ing <math> N </math> degrees of freedom and a choice of associated quantum numbers <math> s_1 \ldots s_N </math>, then an NQS parameterizes the wave-function ...

...at our universe is the only one existing. This theory connects concepts of quantum fluctuations, variable fundamental constants, and the hierarchical arrangem ...eld theory shows that it is not. The vacuum is a dynamic structure full of quantum fluctuations, where virtual particles constantly emerge and disappear. Thes ...

In [[quantum mechanics]], [[angular momentum]] is quantized. The various multipole field == Quantum numbers and selection rules== ...

| known_for = {{ublist|[[Quantum computing]]|[[Loss–DiVincenzo quantum computer]]| [[DiVincenzo's criteria]]}} .../spectrum.ieee.org/david-divincenzo-on-his-tenure-at-ibm-and-the-future-of-quantum-computing |date=2 October 2015 |work=[[IEEE Spectrum]] |access-date=14 Dece ...

In [[quantum mechanics]], the '''quantum revival'''<ref> | title = Periodic spontaneous collapse and revival in a simple quantum model ...

Notably, Gromov-Witten invariants are generally rational numbers while Gopakumar-Vafa invariants are always integers. == As a partition function in topological quantum field theory == ...

...nal|last1=Cassinelli|first1=G.|last2=Lahti|first2=P.|date=2017-11-13|title=Quantum mechanics: why complex Hilbert space?|journal=[[Philosophical Transactions ...ch the Hilbert space is defined] is forced to be the real numbers, complex numbers or quaternions.<ref name=":1" /></blockquote>Writing a decade after Solèr's ...

...rotational states in which specific terms in the molecular [[Hamiltonian (quantum mechanics)|Hamiltonian]] and involving couplings between [[Angular momentum *<math>\mathbf L</math>, the [[Azimuthal quantum number#Angular momentum quantum number|electronic orbital angular momentum]] ...

...] from a pure [[Black-body radiation|black-body spectrum]]. As a result of quantum effects, an isolated black hole emits radiation that, at the black-hole hor ...mega) </math> and with [[Azimuthal quantum number|angular momentum quantum numbers]] <math>\ell, m</math> is given by<ref>{{cite journal |last1=Aharony |firs ...

...[[complex number]]s, and [[complete valued field]]s (such as the [[p-adic numbers|''p''-adic number]]s). ===Real and complex numbers=== ...

{{short description|Model for quantum noise in quantum systems}} .... The <math>d</math>-dimensional depolarizing channel can be viewed as a [[Quantum channel|completely positive trace-preserving map]] <math>\Delta_\lambda</ma ...

...supergravity, speculated by [[Stephen Hawking]], is the most [[symmetric]] quantum field theory which involves gravity and a finite number of fields. It can b ...guish particles with negative spin. These numbers are simple combinatorial numbers that come from [[Pascal's Triangle]] and also the number of ways of writing ...