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Operators Redux (Worksheet)

  • Page ID
    39217
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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?


    This page titled Operators Redux (Worksheet) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Nancy Levinger.

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