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    Ψ1 = sin(𝑘𝑥)

    and

    Ψ2 = e^𝑖𝑘𝑥 = 𝑐𝑜𝑠(𝑘𝑥) + 𝑖sin(𝑘𝑥)

    (i) Determine the action of the linear momentum operator (𝑝̂𝑥 = 𝑖ℏ 𝑑⁄𝑑𝑥) on each wavefunction.

    Not sure how to do this
    thank you
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    (Original post by PencilPot!)
    Ψ1 = sin(𝑘𝑥)

    and

    Ψ2 = e^𝑖𝑘𝑥 = 𝑐𝑜𝑠(𝑘𝑥) + 𝑖sin(𝑘𝑥)

    (i) Determine the action of the linear momentum operator (𝑝̂𝑥 = 𝑖ℏ 𝑑⁄𝑑𝑥) on each wavefunction.

    Not sure how to do this
    thank you
    apply the operator to each wavefunction, as it says in the question:

    𝑝̂ Ψ1 = 𝑖ℏ 𝑑⁄𝑑𝑥 (sin(𝑘𝑥)) = 𝑖ℏ 𝑑(sin(𝑘𝑥)) ⁄𝑑𝑥
    now do the maths (ie differentiate sin(kx) wrt x and you are done with the first one
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    (Original post by MexicanKeith)
    apply the operator to each wavefunction, as it says in the question:

    𝑝̂ Ψ1 = 𝑖ℏ 𝑑⁄𝑑𝑥 (sin(𝑘𝑥)) = 𝑖ℏ 𝑑(sin(𝑘𝑥)) ⁄𝑑𝑥
    now do the maths (ie differentiate sin(kx) wrt x and you are done with the first one
    Thank you very much!
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    (Original post by PencilPot!)
    Thank you very much!
    assuming you've managed both, I'd say it's worth making a comment about whether or not each wavefunction corresponds to an eigenstate of the momentum operator.

    I assume you're pretty new to quantum mechanics, so if you have any questions about what those things mean then do ask
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    (Original post by MexicanKeith)
    assuming you've managed both, I'd say it's worth making a comment about whether or not each wavefunction corresponds to an eigenstate of the momentum operator.

    I assume you're pretty new to quantum mechanics, so if you have any questions about what those things mean then do ask
    Haha! that was the next question - Atkins is quite good at explaining this part

    Yep, I've only just started Quantum...

    And thank you!
 
 
 
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