In A Particle in a Box- 1 we have seen that we can write the quantum state of a particle in a box in the eigen-basis of energy operator. From now on we will call this the Hamiltonian operator. For a recap the eigenvalue equation for the Hamiltonian for a particle in a box system is

$latex \hat H \left| \phi_n\right\rangle = E_n \left|\phi_n\right\rangle&s=2$

with

$latex \left\langle \phi_n|\phi_m\right\rangle=\delta_{nm}&s=2$

and

$latex \sum_{n=1}^{\infty} \left|\phi_n\right\rangle\left\langle\phi_n\right|=\hat I&s=2$

With this we could write any arbitrary state of the system as

$latex \left|\psi\right\rangle = \sum_{n=1}^{\infty} \left|\phi_n\right\rangle\left\langle\phi_n|\psi\right\rangle&s=2$

Here $latex \left\langle\phi_n|\psi\right\rangle$ are the expansion coefficients (or probability amplitudes) whose modulus square  $latex |\left\langle\phi_n|\psi\right\rangle|^2$ is the probability that upon measurement the system will return energy $latex E_n$ associated with the eigenvector $latex \left|\phi_n\right\rangle$.

Lets now ask the question

Where is the particle in the box?

To answer this question we need to look first at Position Operator