Native language: EnglishLevel of quantum mechanics: Introductory or beginner

In summary, wavepacket is a localized wavefunction which has more or less energy at the average position.
  • #1
Alice Jin
18
0
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.
 
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  • #2
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

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.
 

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  • #3
Alice Jin said:
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:

https://www.physicsforums.com/showthread.php?t=265538
 
  • #4
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.
 
  • #5
well do you understand my answer?
 
  • #6
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?
 
  • #7
Alice Jin said:
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?
 

1. What is the difference between a wavepacket and a wavefunction?

A wavepacket is a localized wave that represents the probability amplitude of a particle in a specific region of space. It is a combination of multiple waves with different frequencies and wavelengths. A wavefunction, on the other hand, is a mathematical description of the state of a quantum system, including the position and momentum of a particle. It is a solution to the Schrödinger equation and can be used to calculate the probability of finding a particle in a certain location.

2. How are wavepackets and wavefunctions related?

A wavepacket can be thought of as a superposition of multiple wavefunctions. The wavepacket represents the probability of finding a particle in a specific region of space, while the wavefunction describes the overall state of the particle. The shape and behavior of a wavepacket are determined by the properties of the underlying wavefunctions.

3. Can a wavepacket and a wavefunction be equivalent?

No, a wavepacket and a wavefunction are not equivalent. While they are related, they serve different purposes and have different properties. A wavepacket is a physical representation of a particle, while a wavefunction is a mathematical description of the particle's state.

4. How does the shape of a wavepacket affect its behavior?

The shape of a wavepacket determines the spread or localization of the particle's position. A narrower wavepacket indicates a more localized particle, while a wider wavepacket suggests a more spread-out particle. Additionally, the shape of a wavepacket can also affect the particle's momentum and energy.

5. Are wavepackets and wavefunctions applicable to all types of waves?

No, wavepackets and wavefunctions are specific to quantum mechanics and are used to describe the behavior of particles at a microscopic level. They do not apply to classical waves, such as sound or light, which can be described by different equations and do not exhibit quantum phenomena.

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