Infinite potential well problem normalization

In summary: Guys, Thank you soo much. I've got a passing grade. It is mind boggling to see myself perform childish mistakes doing advanced quantum physics. I am currently analyzing reasons responsible for such performance.
  • #1
Ashish Somwanshi
31
4
Homework Statement
Suppose an electron in an infinite potential well with width, L, has a wavefunction,
ϕ(z)=Az(z−L) for 0<z<L
Normalize this wavefunction and derive an expression for the constant A in terms of L.
Relevant Equations
∫|ψ(x,t)|^2dx=1, integral lower bound: minus infinity
Upper bound: positive infinity
I have attached my attempt and proof that my attempts were incorrect.
 

Attachments

  • images.jpeg
    images.jpeg
    31.6 KB · Views: 104
  • Screenshot_20221002_231727.jpg
    Screenshot_20221002_231727.jpg
    21.7 KB · Views: 94
  • Homework attempt.pdf
    663.8 KB · Views: 92
  • Screenshot_20221002_234217.jpg
    Screenshot_20221002_234217.jpg
    22.8 KB · Views: 94
Last edited:
Physics news on Phys.org
  • #2
According to the homework guidelines you must make your best attempt at this before we can help.
 
  • #3
PeroK said:
According to the homework guidelines you must make your best attempt at this before we can help.
 

Attachments

  • Homework attempt.pdf
    429.6 KB · Views: 114
  • #4
Your method is fine. Double check your final calculations- using ##60## as a common denominator, perhaps.
 
  • #5
PeroK said:
Your method is fine. Double check your final calculations- using ##60## as a common denominator, perhaps.
Yeah, dosen't work. Please do provide your solution.
 
Last edited by a moderator:
  • #6
Ashish Somwanshi said:
Yeah, dosen't work. Plz do provide your solution.
Screenshot_20221002_233441.jpg
 
  • #7
Ashish Somwanshi said:
Yeah, dosen't work. Plz do provide your solution.
This is my final attempt despite using 60 as common denominator.
 

Attachments

  • Screenshot_20221002_234217.jpg
    Screenshot_20221002_234217.jpg
    21.7 KB · Views: 92
  • #8
Ashish Somwanshi said:
This is my final attempt despite using 60 as common denominator.
Okay, let's try this again. ##\dfrac{1}{5} - \dfrac{2}{4} + \dfrac{1}{3}## is what?

-Dan
 
  • Like
Likes PeroK
  • #9
topsquark said:
Okay, let's try this again. ##\dfrac{1}{5} - \dfrac{2}{4} + \dfrac{1}{3}## is what?

-Dan
Sorry, I don't understand how to add three fractions using common denominator, in my first attempt I did the old way but still incorrect. Plz do provide the solution if anyone can solve their way. Either the autograder must be faulty or something I must be missing...
 
  • #10
topsquark said:
Okay, let's try this again. ##\dfrac{1}{5} - \dfrac{2}{4} + \dfrac{1}{3}## is what?

-Dan
It's 1/12 according to evaluating two fractions one at a time.
 
  • Skeptical
Likes berkeman
  • #11
Ashish Somwanshi said:
Plz do provide the solution if anyone can solve their way.
No, we do not provide solutions. You really don't understand how to add those fractions? Also, please do not use text speak at PF like "please". Thank you.
 
  • Like
Likes topsquark
  • #12
I will redo the solution as I have made silly mistakes in evaluating the fractions...Thanks for spotting it.
 
  • #13
Ashish Somwanshi said:
I will redo the solution as I have made silly mistakes in evaluating the fractions...Thanks for spotting it.
Guys, Thank you soo much. I've got a passing grade. It is mind boggling to see myself perform childish mistakes doing advanced quantum physics. I am currently analyzing reasons responsible for such performance.
 
  • Like
Likes PeroK

Related to Infinite potential well problem normalization

What is the infinite potential well problem normalization?

The infinite potential well problem normalization is a mathematical technique used in quantum mechanics to find the probability of a particle being in a certain position within a confined space. It is commonly used to solve problems involving particles in a one-dimensional box with infinite potential walls.

Why is normalization important in the infinite potential well problem?

Normalization is important because it ensures that the total probability of finding a particle within the well is equal to 1. This means that the particle must be somewhere within the well, and the probability of finding it at any point is not greater than 1.

How is the wave function normalized in the infinite potential well problem?

The wave function is normalized by finding the normalization constant, which is the square root of the integral of the wave function squared over the entire well. This constant is then multiplied by the original wave function to ensure that the total probability is equal to 1.

Can the normalization constant be negative in the infinite potential well problem?

No, the normalization constant must be a positive value. This is because the wave function squared represents the probability density, and probabilities cannot be negative. If the normalization constant were negative, it would result in a negative probability, which is not physically meaningful.

What happens if the wave function is not normalized in the infinite potential well problem?

If the wave function is not normalized, the total probability of finding the particle within the well will be greater than 1. This means that the particle could potentially be found outside of the well, which is not possible in the infinite potential well problem. Normalization is necessary to ensure that the results of the problem are physically accurate.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
711
  • Introductory Physics Homework Help
Replies
18
Views
2K
  • Introductory Physics Homework Help
Replies
27
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
783
  • Introductory Physics Homework Help
Replies
2
Views
598
  • Introductory Physics Homework Help
2
Replies
64
Views
2K
  • Introductory Physics Homework Help
Replies
23
Views
479
  • Introductory Physics Homework Help
Replies
2
Views
507
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
485
Back
Top