Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$

Question

This is probably a simple question, but what does the subscript $0$ mean in the following expression?

$$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$

Answer 1

The subscript zero here probably just means either

1. that one should put $q=0$ after differentiating twice,

2. or that the Hessian $\left. \partial_i\partial_j V \right|_{q=q_{(0)}}$ is evaluated at point $q_{(0)}$ that is a stationary point $\left. \partial_i V \right|_{q=q_{(0)}}=0$.

One would have to see the precise context to be sure.

Answer 2

Usually that means "initial" or if you're in Europe it can mean either "nought" or initial. All three mean the same thing though. An example would be $v_0$ which would be initial velocity.

Edit:

The zero subscript does not HAVE to mean initial. As I mentioned in a comment, we can take an example from electrostatics where epsilon nought ($ε_0$) is the permittivity of free space, not any initial value.