• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Finding fourier transfrom of the following wavefunction

  • Thread starter Feynmanfan
  • Start date
129
0
Let Psi(x,0)=E^(ik0x) when x=(-a/2,a/2) and zero elsewhere.

Can this be a wavefunction of a free particle. I belive it is so because every function of x can be expressed as a wavepacket. Is this correct?

If I want to calculate P(x,0), probability to find the particle between x, x+dx it's just the square of the modulus. But what about P(k,0)? I'm having trouble calculating it's fourier transform, I think that the delta function must show somewhere but I don't know how.

k seems to be certain k=k0 , right? However, P(x,0)=1/a is the same everywhere.
 

OlderDan

Science Advisor
Homework Helper
3,021
1
Feynmanfan said:
Let Psi(x,0)=E^(ik0x) when x=(-a/2,a/2) and zero elsewhere.

Can this be a wavefunction of a free particle. I belive it is so because every function of x can be expressed as a wavepacket. Is this correct?

If I want to calculate P(x,0), probability to find the particle between x, x+dx it's just the square of the modulus. But what about P(k,0)? I'm having trouble calculating it's fourier transform, I think that the delta function must show somewhere but I don't know how.

k seems to be certain k=k0 , right? However, P(x,0)=1/a is the same everywhere.
If k_0 is one definite value, then the particle has one precise momentum. What does the uncertainty principle say about the position of such a particle?
 

dextercioby

Science Advisor
Homework Helper
Insights Author
12,950
532
Is the wavefunction normalizable...?It is a generalized eigenfunction of the Hamiltonian...?

Daniel.
 
129
0
Yes it is normalizable. But it's not a generalized function of the Hamiltonian, is it? It's a particular case where k=ko.

I'm asked to draw P(x,0) and P(k,0) and find out delta(x) and delta(k) and justify it using Heisenberg's uncertainty principle.

By doing Psi's Fourier transform I get a complicated function and I don't know if that's the way I can justify the following: we know nothing about the position (cause all probabilities are the same) but k is certain.
 

Related Threads for: Finding fourier transfrom of the following wavefunction

Replies
5
Views
359
  • Posted
Replies
2
Views
1K
Replies
3
Views
442
  • Posted
Replies
2
Views
1K
  • Posted
Replies
2
Views
4K
  • Posted
Replies
3
Views
1K
Replies
2
Views
938
  • Posted
Replies
12
Views
1K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top