The principal quantum number, n, describes the energy of the electron and is always a positive integer.

The azimuthal quantum number,, describes the orbital angular momentum of each electron and is a non-negative integer.

The magnetic quantum number,, describes the magnetic moment of an electron in an arbitrary direction, and is also always an integer.

The quantum Hall effect was discovered by Klaus von Klitzing in 1980 when he observed the Hall conductivity to be integer multiples of a fundamental constant.

According to Professor Gilles Brassard, an expert in quantum computing: " The time needed to factor an RSA integer is the same order as the time needed to use that same integer as modulus for a single RSA encryption.

The spin-statistics theorem holds that, in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.

In contrast, particles with integer spin ( called bosons ) have symmetric wave functions ; unlike fermions they may share the same quantum states.

According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states ; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.

Large-scale quantum computers could be able to solve certain problems much faster than any classical computer by using the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems.

This ability would allow a quantum computer to decrypt many of the cryptographic systems in use today, in the sense that there would be a polynomial time ( in the number of digits of the integer ) algorithm for solving the problem.

If one used Planck's energy quanta, and demanded that electromagnetic radiation at a given frequency could only transfer energy to matter in integer multiples of an energy quantum hν, then the photoelectric effect could be explained very simply.

Shor's algorithm, named after mathematician Peter Shor, is a quantum algorithm ( an algorithm which runs on a quantum computer ) for integer factorization formulated in 1994.

On a quantum computer, to factor an integer N, Shor's algorithm runs in polynomial time ( the time taken is polynomial in log N, which is the size of the input ).

Specifically it takes time, demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is thus in the complexity class BQP.

The quantum Hall effect ( or integer quantum Hall effect ) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductivity σ takes on the quantized values

The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively.

It is also very well understood as an integer quantum Hall effect, not of electrons but of charge-flux composites known as composite fermions.

Actual measurements of the Hall conductance have been found to be integer or fractional multiples of e < sup > 2 </ sup >/ h to nearly one part in a billion.

The integer quantization of the Hall conductance was originally predicted by Ando, Matsumoto, and Uemura in 1975, on the basis of an approximate calculation which they themselves did not believe to be true.

Most integer quantum Hall experiments are now performed on gallium arsenide heterostructures, although many other semiconductor materials can be used.

In 2007, the integer quantum Hall effect was reported in graphene at temperatures as high as room temperature, and in the oxide ZnO-Mg < sub > x </ sub > Zn < sub > 1-x </ sub > O.

The colors represent the integer Hall conductances.

The observed strong similarity between integer and fractional quantum Hall effects is explained by the tendency of electrons to form bound states with an even number of magnetic flux quanta, called composite fermions.

Klaus von Klitzing ( 28 June 1943 in Schroda ) is a German physicist known for discovery of the integer quantum Hall Effect, for which he was awarded the 1985 Nobel Prize in Physics.

This level is responsible for the anomalous integer quantum Hall effect.

As in the integer quantum Hall effect, a series of plateaus form in the Hall resistance.

A Hall divisor of an integer n is a divisor d of n such that

In effect, integer size sets a hardware limit on the range of integers the software run by the CPU can utilize.

( see figure ) The effect was observed to be independent of parameters such as the system size and impurities, and in 1981, theorist Robert Laughlin proposed a theory describing the integer states in terms of a topological invariant called the Chern number.

The effect of the prefixes is to multiply or divide the unit by a factor of ten, one hundred or an integer power of one thousand.

There are an infinite number of irrational reciprocal pairs that differ by an integer ( giving the curious effect that the pairs share their infinite mantissa ).

This has the effect of keeping the middle bits ; the < var > I </ var >- number of least significant integer bits, and the < var > Q </ var >- number of most significant fractional bits.

The Dirac string acts as the solenoid in the Aharonov-Bohm effect, and the requirement that the position of the Dirac string should not be observable implies the Dirac quantization rule: the product of a magnetic charge and an electric charge must always be an integer multiple of.

We say that N is nilpotent if there is some positive integer R such that Af.

In litters of eight mice from similar parents, the number of mice with straight instead of wavy hair is an integer from 0 to 8.

In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients ( or equivalently — by clearing denominators — with integer coefficients ).

All numbers which can be obtained from the integers using a finite number of integer additions, subtractions, multiplications, divisions, and taking nth roots ( where n is a positive integer ) are algebraic.

An algebraic integer is an algebraic number which is a root of a polynomial with integer coefficients with leading coefficient 1 ( a monic polynomial ).

# There is always an integer number of electrons orbiting the nucleus.

Within a shell where n is some integer n < sub > 0 </ sub >, ranges across all ( integer ) values satisfying the relation.

Within a subshell where is some integer, ranges thus:.

In other words, there is no program which takes a string s as input and produces the integer K ( s ) as output.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).