Infinitesimal momentum element

Question

I understand that $d^3x$ is an infinitesimal volume element. But how do I physically make sense of $d^3p$, the momentum element?

Young Kindaichi · Answer

Well, Of course, You can't visualize the Six-dimensional phase space living in the $3$-D. But it's always useful to take examples of lower dimensions. For particles in one dimension, The phase space is $2$-D and can be drawn. In this case, The phase space volume
$$Delta  V=Delta qDelta p$$
which is just the area of the square shown below.

You can think of doing the same thing in higher dimensions.

Infinitesimal momentum element

One Answer

Add your own answers!

Ask a Question