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Operators Redux (Worksheet)

Last updated

Jul 3, 2021
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- Operators and Eigenvalues (Worksheet)
- Particle in a Box Probability (Worksheet)

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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?

Preamble

Q1

Q2

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