The derivative of this quantity with respect to height appears in the definition of the Brunt-Vaisala frequency.
The Wigner function is, up to a constant factor, the Weyl transform of an operator with this name. That operator with this name is multiplied by an observable, then the trace is taken, to find the expectation value of that observable, and more generally is used to represent mixed quantum states. The derivative of this quantity with respect to height appears in the definition of the Brunt-Vaisala frequency. The speed of sound for a solid is equal to the square root of the (*) bulk modulus over this quantity. The pressure difference in a u-shaped column is equal to this quantity times g times the difference in height. The fact that this quantity is different for silver and gold led to the formulation of Archimedes principle. For 10 points, name this quantity, which for an object is equal to mass over volume.
The Wigner function is, up to a constant factor, the Weyl transform of an operator with this name.
density