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
With this we could write any arbitrary state of the system as
Here are the expansion coefficients (or probability amplitudes) whose modulus square is the probability that upon measurement the system will return energy associated with the eigenvector .
Lets now ask the question
Where is the particle in the box?
To answer this question we need to look first at Position Operator