0
votes
0answers
67 views

Matrix element of an operator

Suppose we want to calculate the following matrix element. $$ \langle \alpha |\hat{o}|\beta\rangle $$ Where $\alpha$ and $\beta$ are two arbitrary basis states in a many-particle basis set, and ...
0
votes
0answers
49 views

How do I find the unitary operator for a combined system?

I want to describe the interaction between a target and a probe and know that this is described by some unitary operator that acts on both systems. My operator needs to implement a $\pi/q$ rotation ...
3
votes
4answers
689 views

Is the momentum operator well-defined in the basis of standing waves?

Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely $$ \left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ...
3
votes
2answers
208 views

How to express continuous values as a matrix

Usually a quantity of a matrix is defined as the eigenvalues of the matrix. If so, how can anyone express continuous values, as in Schrodinger picture, into a matrix?