Normalise Wave Packet psi(x) to Unity

  • Thread starter ak416
  • Start date
  • Tags
    Unity
In summary, the task is to normalize the wave packet psi(x, t=0) = C*exp(i*p0*x/hbar)*exp(-[x]/(2*deltax)) by finding the appropriate value for the normalization constant C such that the integral from negative infinity to positive infinity of ([psi]^2)dx is equal to 1. However, the integral should be done correctly and not result in 0.
  • #1
ak416
122
0
consider the wave packet psi(x, t=0) = C*exp(i*p0*x/hbar)*exp(-[x]/(2*deltax))
where C is the normalisation constant
part a) normalise psi(x) to unity
I took Integral from negative infinity to positive infinity of ([psi]^2)dx and got [C]^2 * ( Integral from negative infinity to 0 of exp(x/deltax)dx + Integral from 0 to positive infinity of exp(-x/deltax)dx )
However this gives me [C]^2 * 0 and there is no number for C that i can think of that can make it equal to 1. I am thinking C must be some complex number, but i don't know where to go from here...
Note: this is for a introductory QM class
 
Physics news on Phys.org
  • #2
You did the integrals wrong. The result is not 0.
 

1. What does it mean to "normalise" a wave packet?

Normalisation refers to the process of adjusting the amplitude of a wave function to ensure that the total probability of finding a particle within a given space is equal to one. This ensures that the wave function obeys the principles of quantum mechanics.

2. Why is it important to normalise a wave packet?

Normalising a wave packet is important because it allows us to accurately calculate the probability of finding a particle within a given space. It also ensures that the wave function follows the fundamental principles of quantum mechanics, such as conservation of probability.

3. How do you normalise a wave packet to unity?

To normalise a wave packet to unity, we need to find the appropriate normalisation constant that will adjust the amplitude of the wave function. This constant can be calculated by taking the square root of the integral of the square of the wave function over all space. We then divide the wave function by this constant to obtain a normalised wave function with a total probability of one.

4. Can a wave packet be normalised to a value other than unity?

Yes, a wave packet can be normalised to any value as long as it is a positive real number. However, normalising to unity is the most common practice as it allows for easier calculations of probabilities and follows the principles of quantum mechanics.

5. What happens if a wave packet is not normalised?

If a wave packet is not normalised, it means that the total probability of finding a particle within a given space is not equal to one. This can lead to incorrect calculations of probabilities and violates the principles of quantum mechanics. Therefore, it is important to always normalise a wave packet before performing any calculations.

Similar threads

  • Advanced Physics Homework Help
Replies
10
Views
582
  • Advanced Physics Homework Help
Replies
2
Views
894
  • Advanced Physics Homework Help
Replies
5
Views
988
  • Advanced Physics Homework Help
Replies
7
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
10
Views
450
  • Advanced Physics Homework Help
Replies
1
Views
876
  • Advanced Physics Homework Help
Replies
6
Views
2K
Replies
16
Views
555
  • Advanced Physics Homework Help
Replies
3
Views
889
Back
Top