# Conjugate variables facts for kids

**Conjugate variables** are special pairs of variables (like x, y, z) that don't give the same result when you do a certain mathematical operation with them. This means that x*y is not equal to y*x. Here, the * does not mean multiplication. It could mean addition, subtraction, division, or any operation that makes sense, in that case.

A physicist, Werner Heisenberg, and his co-workers used equations studied in classical physics to describe and predict events from quantum physics. He discovered that the momentum (mass times velocity, represented by **P**) and position (represented by **Q**) are conjugate variables. This means that **P*Q** is not equal to **Q*P,** in quantum physics.

Here are two special equations to calculate the energy of an electron (small green thing) in a hydrogen atom.

The first equation could be used to find out the product of momentum and position:

The second equation could be used to calculate the product of position and momentum:

Some time later, another physicist, Max Born found out that, because **P*Q** is not equal to **Q*P,** the result of **Q*P** minus **P*Q** is not zero. (The "minus" is not the same minus of "3 - 2". It's a different thing with the same name).

Born found out that:

[The symbol **Q** is the matrix for position, **P** is the matrix for momentum, **i** is a complex number, and **h** is Planck's constant, a number that shows up in quantum mechanics a lot.]

Conjugate variables have applications all over Physics, in Chemistry and in a bunch of other areas of science.

Myrlie Evers-Williams |

Aaron Henry |

T. R. M. Howard |

Jesse Jackson |

*Kiddle Encyclopedia.*