Momentum/angle values of eigenstates in a graphene system

[FermiDIrac19]

I am trying to differentiate between states in a quantum system of graphene with open boundaries in one direction and periodic boundaries in the other direction.
The eigenstates have been simulated with the eigenenergies, but how would I proceed in calculating the expectation value of the momentum in x- and y- direction in order to deduce an angle associated with each eigenstate?

 

[BigJDubs]

To calculate the expectation value of the momentum in x- and y- directions, you will need to first calculate the expectation values of the momentum operators $\hat{P}_x$ and $\hat{P}_y$. These operators can be expressed as follows:$$\hat{P}_x = \frac{\hbar}{i} \left(\frac{\partial}{\partial x}\right)$$ $$\hat{P}_y = \frac{\hbar}{i} \left(\frac{\partial}{\partial y}\right)$$Once you have these operators, you can then calculate the expectation values for each eigenstate by taking the inner product of the state with the operator, i.e. $$\langle \psi | \hat{P}_x | \psi \rangle$$$$\langle \psi | \hat{P}_y | \psi \rangle$$where $\psi$ is the eigenstate and $\hat{P}_x$ and $\hat{P}_y$ are the momentum operators. Once you have the expectation values for each eigenstate, you can then calculate the angle associated with each eigenstate by using the following formula:$$\theta = \tan^{-1} \left(\frac{P_y}{P_x}\right) $$where $P_x$ and $P_y$ are the expectation values of the momentum in x- and y- directions for the given eigenstate.