Wavepacket vs. wavefunction

[Alice Jin]

Dear,

I have a trouble understanding QM.
What's the difference between wavepacket and wavefunction?
Can we use a wavepacket for a particle in a box?
Please reply to this questions.
Thank you in advance.

[ice109]

a wavepacket is a wavefunction which is localized, meaning really high in some small region and small everywhere else. a wavefunction is just slang for a solution to the shrodinger eqn.

here's a wavepacket

http://www.codersource.net/published/view/279/Coder_Source_Gaussian_Blur_Smoothing_gauss1.gif

see how it's really high around x=0 and hence it's square, which is the probability amplitude, in a very small range and zero everywhere else. hence the particle which this wave packet describes is most likely to have energy around x=0. therefore the energy is in some sense localized.

here's another wave function

http://www.libraryofmath.com/pages/graphs-of-sine-and-cosine/Images/graphs-of-sine-and-cosine_gr_46.gif

the range of values where it's high, and hence it's probability amplitude is high, is just plain weird. hence you couldn't say it's energy is localized.

really there's no difference between the two, it's slang. so if you want you can call the solution to the shrodinger eqn for a particle in a box a wavepacket, bob, or whatever you want- as long as you write down the correct mathematical formula.

[olgranpappy]

Dear,

I have a trouble understanding QM.
What's the difference between wavepacket and wavefunction?
Can we use a wavepacket for a particle in a box?
Please reply to this questions.
Thank you in advance.

uhh... didn't you just ask this same question here:

http://www.physicsforums.com/showthread.php?t=265538

[Alice Jin]

Yeah, I did. But I'm not quiet sure about the wavepacket. That's why I asked different subject. Also I think it's different thing.

[ice109]

well do you understand my answer?

[Alice Jin]

Thanks, ice109.

What you're saying is that the wavepacket has more or less localized energy at the average position even though the wavepacket is composed of lots of different momenta and for the wavefuction I can consider it like the excited state of paticle in a box. Right?
Am I understood?

[ice109]

Thanks, ice109.

What you're saying is that the wavepacket has more or less localized energy at the average position even though the wavepacket is composed of lots of different momenta and for the wavefuction I can consider it like the excited state of paticle in a box. Right?
Am I understood?

you are understood but you've misunderstood me. so first tell me what is your native language and what level of quantum mechanics are you studying?