# Group Work 3: Operators

- Page ID
- 31873

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

*Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.*

### Preamble

The order that operators are applied to a function can be **very important**.

### Q1

Suppose that

\[\hat{A}=\dfrac{d}{dx} \tag{W.1}\]

and

\[\hat{B}=x^2 \tag{W.2}\]

For any function \(f(x)\) what is \(\hat{A}f(x)\)?

What is \(\hat{B}f(x)\)?

What is \(\hat{A}\hat{B}f(x)\)?

What is \(\hat{B}\hat{A}f(x)\)?

Is \(\hat{A}\hat{B}f(x)=\hat{B}\hat{A}f(x)\)? Why?

When \(\hat{A}\hat{B}f(x)=\hat{B}\hat{A}f(x)\), the two operators *commute. *Do \(\hat{A}=\dfrac{d}{dx}\) and \(\hat{B}=x^2\) commute?

### Q2

Suppose that

\[\hat{A}=\dfrac{d}{dx} \tag{W.3}\]

and

\[\hat{B}=10 \tag{W.4}\]

What is \(\hat{A}f(x)\)?

What is \(\hat{B}f(x)\)?

What is \(\hat{A}\hat{B}f(x)\)?

What is \(\hat{B}\hat{A}f(x)\)?

Do \(\hat{A}\) and \(\hat{B}\) commute?