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# Wave-functions help! watch

1. 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
2. (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
3. (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!
4. (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
5. (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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Updated: October 18, 2017
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