Maximizing Learning: The Importance of Showing Your Work in Problem Solving

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SUMMARY

The discussion centers on solving a homework problem involving an electron in a finite potential well with a depth of V0=0.3 eV and a width of 10 nm. Participants clarify that the formula E(n) = n²*h²/(8mL²) is applicable for infinite potential wells, not finite ones, and emphasize the need for numerical techniques to find energy levels in finite wells. The correct approach involves using the cotangent function to find intersections for energy levels, which led to successful calculations for both the ground and second energy states. The importance of showing work in electronic homework systems is also highlighted, as it aids in understanding and troubleshooting errors.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically potential wells.
  • Familiarity with the formula E(n) = n²*h²/(8mL²) for energy levels.
  • Knowledge of numerical techniques for solving transcendental equations.
  • Proficiency in using graphing tools like Desmos for visualizing functions.
NEXT STEPS
  • Research "finite potential well" to understand energy calculations in finite systems.
  • Learn about numerical methods for solving transcendental equations in quantum mechanics.
  • Explore MATLAB programs for simulating quantum systems and potential wells.
  • Study the cotangent function's role in finding energy levels in finite potential wells.
USEFUL FOR

Students studying quantum mechanics, particularly those tackling problems related to finite potential wells, as well as educators seeking to improve homework feedback methods in electronic systems.

Ashish Somwanshi
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Homework Statement
Consider an electron in a finite potential with a depth of V0=0.3eV and a width of 10nm.
i) Find the lowest energy level?
ii) Find the second lowest energy level?

Give your answer in unit of eV. Answers within 5% error will be considered correct.

Note that in the lecture titled "Finite Potential Well", the potential well is defined from −L to L, which makes the well width 2L. Plz help solve this homework problem. The answer of 0.03769*10^(-9) mev is incorrect. I have also attached the screenshot
Relevant Equations
E(n) = n^2*h^2/(8mL^2)
images (2).jpeg
 

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Ashish Somwanshi said:
Homework Statement:: Consider an electron in a finite potential with a depth of V0=0.3eV and a width of 10nm.
i) Find the lowest energy level?
ii) Find the second lowest energy level?

Give your answer in unit of eV. Answers within 5% error will be considered correct.

Note that in the lecture titled "Finite Potential Well", the potential well is defined from −L to L, which makes the well width 2L. Plz help solve this homework problem. The answer of 0.03769*10^(-9) mev is incorrect. I have also attached the screenshot of incorrect message by autograder.
I do not understand where I went wrong? Formula is correct? It's application is correct and the answer I got in joule I converted to mev by dividing it by 1.6*10^-19 as you can clearly see in my work? Then how come autograder reject the answer?
Ashish Somwanshi said:
Relevant Equations:: E(n) = n^2*h^2/(8mL^2)

View attachment 314956
 
Welcome to PF!

It seems you are using the formula for the ground state of an infinite potential well to calculate the ground state of a finite potential well. If you review your notes you should see that there is a numerical technique to calculate the ground state when the well is finite. This is why they allowed a 5% variance in the answer I believe.
 
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bob012345 said:
Welcome to PF!

It seems you are using the formula for the ground state of an infinite potential well to calculate the ground state of a finite potential well. If you review your notes you should see that there is a numerical technique to calculate the ground state when the well is finite. This is why they allowed a 5% variance in the answer I believe.
These are my notes till potential step starting from the finite potential problem. I don't see any numerical technique or formula for energy similar to infinite potential problem. Plzz do show me the numerical technique if it exist...
 
Ashish Somwanshi said:
These are my notes till potential step starting from the finite potential problem. I don't see any numerical technique or formula for energy similar to infinite potential problem. Plzz do show me the numerical technique if it exist...
There is plenty on the web. Just search "finite potential well." Start with the Wikipedia article.
 
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Ashish Somwanshi said:
These are my notes till potential step starting from the finite potential problem. I don't see any numerical technique or formula for energy similar to infinite potential problem. Plzz do show me the numerical technique if it exist...
Sorry, I do not see the link to your notes but the formula you are using is valid for potential wells of infinite depth not finite depth like 0.3eV. I am not sure how your teacher presented this material but here are some notes I found;

http://ursula.chem.yale.edu/~batista/classes/vvv/FiniteSquareWell.pdf
 
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Unfortunately, I'm not able to view the contents of link maybe some issue with the website. Can you please upload the square well pdf on the forum. I will download and study it in detail.
 
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Ashish Somwanshi said:
Unfortunately, I'm not able to view the contents of link maybe some issue with the website. Can you please upload the square well pdf on the forum. I will download and study it in detail.
Try this link then. If you can't get to it just do a search on Finite Potential Well.

https://ph.qmul.ac.uk/sites/default/files/finitewell.pdf

What level is your class?
 
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  • #10
Searching on the net I found some material on finite potential well from Purdue University and there they solve the same problem of the width 10nm and Vo=0.3 eV using a MATLAB program. I entered those answers but they got rejected by the autograder. How is this possible?
 

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  • #11
It is possible that you made a mistake somewhere. We cannot tell you where you made a mistake merely by looking at the answer you found. You need to show us the details of your calculation. If it's a MATLAB program that you found on the web and just used, (a) how do you know you can trust it and (b) how do you know you used it correctly?
 
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  • #12
Ashish Somwanshi said:
Searching on the net I found some material on finite potential well from Purdue University and there they solve the same problem of the width 10nm and Vo=0.3 eV using a MATLAB program. I entered those answers but they got rejected by the autograder. How is this possible?
Yes, please show us how you got the numbers. Sometimes those auto graders can be quite particular. Also, you can solve the two transcendental equations graphically in the Desmos Graphing Calculator.
 
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  • #13
The quiz mentions 'the lecture titled "Finite Potential Well".' This is probably where you should be looking to find how to solve this,
 
  • #14
Another thing to check is your units and conversions in your calculations. Your ground state value is roughly ten times larger than what it should be given the depth and width of the well.
 
  • #15
Ashish Somwanshi said:
Homework Statement:: Consider an electron in a finite potential with a depth of V0=0.3eV and a width of 10nm.
i) Find the lowest energy level?
ii) Find the second lowest energy level?

Give your answer in unit of eV. Answers within 5% error will be considered correct.

Note that in the lecture titled "Finite Potential Well", the potential well is defined from −L to L, which makes the well width 2L. Plz help solve this homework problem. The answer of 0.03769*10^(-9) mev is incorrect. I have also attached the screenshot
Relevant Equations:: E(n) = n^2*h^2/(8mL^2)

In the future, please post your work in LaTeX to make it easier for us to read and reply to. There is a "LaTeX Guide" link below the Edit window. Thank you.
 
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  • #16
I got two values of eta

Eta 1=1.466 from which ground state energy was 0.00325 which was correct according to the autograder.
Eta 2 = 4.395 from which second energy was 0.02922, for some reason autograder rejected it. How is it possible for the same method one correct and another incorrect answer?
 

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  • #17
Ashish Somwanshi said:
How is it possible for the same method one correct and another incorrect answer?
Forget the autograder. You have been asked repeatedly to show your method and you have not done that yet. We cannot answer questions about the method if we don't know what it is. The method is either correct or incorrect and you applied it either correctly or incorrectly. That's what counts and that's what you have control over, not the autograder.
 
  • #18
Thanks guys, I've finally solved the question, to find eta value for second energy we had to find intersection of curve with cot(eta) function since it has odd parity and hence find the energy. I've got the correct result for second part of the question as well.
 
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  • #19
kuruman said:
Forget the autograder. You have been asked repeatedly to show your method and you have not done that yet. We cannot answer questions about the method if we don't know what it is. The method is either correct or incorrect and you applied it either correctly or incorrectly. That's what counts and that's what you have control over, not the autograder.
Likewise students are not going to show their work to the teachers much with these electronic homework systems. I have only limited experience but when I taught a physics course some students opted for the ebook and ehomework which I did not really want but had to let them. I preferred the old fashioned paper homework so I could see what the students process was. And while I'm griping about modern teaching methods, the teacher developing material with blackboards and whiteboards is far better than giving the students a PowerPoint presentation.
 

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