This is an old revision of the document!

## Homework for Matrix Components

1. (MatrixElements) This practice exercise helps students understand that they can “pick out” a particular component of a matrix by taking the braket of the matrix with appropriate basis vectors. The “bra” vector picks out the row and the “ket” vector picks out the column. Part $(c)$ requires Dirac bra-ket notation.
1. Carry out the following matrix calculations.

$$\pmatrix{0&1&0\cr}\pmatrix{a_{11} & a_{12} & a_{13} \cr a_{21} & a_{22} & a_{23} \cr a_{31} & a_{32} & a_{33}\cr}\pmatrix{1\cr0\cr0\cr}$$ and

$$\pmatrix{0&1&0\cr}\pmatrix{a_{11} & a_{12} & a_{13} \cr a_{21} & a_{22} & a_{23} \cr a_{31} & a_{32} & a_{33}\cr}\pmatrix{0\cr1\cr0\cr}\quad$$

2. What matrix multiplication would you do if you wanted the answer to be $a_{13}$?

3. The bra-ket language for the calulations in part $(a)$ are

$$\matrix{\langle2|A|1\rangle = ? & \hbox{and} & \langle2|A|2\rangle = ?}$$

Write the question to part $(b)$ in bra-ket language.

##### Views

New Users

Curriculum

Pedagogy

Institutional Change

Publications