0
votes
1answer
84 views

Matrix elements of the operator $\hat{x} \hat{p}$ in position and momentum basis

I want to calculate the matrix elements of the operator $\hat{x} \hat{p}$ in momentum and position basis, that is the two quantities ($p,q$ - momenta, $x,y$ - positions): $$\langle p|\hat{x} ...
4
votes
1answer
40 views

Perturbation of an operator - Meaning of matrix element [closed]

Let be $B$ an operator and $\left|\Psi\right>$, $\left|\Phi\right>$ two states (not necessarily equals). What is the meaning of a matrix element $\left<\Psi\right| B ...
4
votes
1answer
124 views

How are matrices used to represent quantities, and what is the meaning of a matrix?

So I'm reading this text on Quantum Mechanics, and it goes through a few chapters that I understand fairly well including probability. But then it says that all quantities, like position and energy ...
0
votes
0answers
79 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
60 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
773 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
225 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?