# Wolfram Mathematica

## Physical Variables and Quantity Units

With the new improvements in Quantity and QuantityVariable functionality, it is now even simpler to work with derivatives of quantity variables and define new units and physical quantities.

This example explores the canonical units and physical dimensions of terms of equations or general sets of quantity variables.

Separate the terms of the equation for a quantum harmonic oscillator.

Each term has different canonical units but the same dimensions, and therefore all terms are compatible.

Alternatively, you can start with a set of physical quantities of given dimensions, find their canonical units and construct dimensionless combinations.

Take three quantity variables of which you know their physical quantity, or just a list of physical dimensions. A new, independent physical dimension called "Widgets" is introduced, which has its own units and physical quantities.

Find the canonical units associated with those physical quantities.

Determine their unit dimensions.

Find a combination of the variables that matches the dimensions of a specific physical quantity.