Particle in one dimension wave function from Quantum Mechanics

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The discussion revolves around solving a quantum mechanics problem related to a particle's wave function in one dimension. The user expresses uncertainty about how to plot the graph of their solution and mentions using Overleaf LaTeX for plotting. Suggestions include using Excel's ERF function for graphing. Additionally, there is advice on verifying the correctness of their previous answers by troubleshooting and checking the integration results. The conversation emphasizes the importance of self-assessment in problem-solving.
BlondEgg
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Homework Statement
Using various def's in Quantum Mechanics for a particle in one dimension.
Relevant Equations
Wave function
Hi,

I try and solve this problem

1721511249924.png

I have solved the problem in different parts

1721511357658.png

1721511427351.png

But me not sure how to plot the graph. Maybe someone knows?

Merci
 
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BlondEgg said:
But me not sure how to plot the graph. Maybe someone knows?
With a plotting program? Excel has the ERF function that you can use.
 
kuruman said:
With a plotting program? Excel has the ERF function that you can use.
merci

I plotted in overleaf latex

1721513497875.png

Do you know if the other parts (i) (ii) (iii) (iv) are good?

Best wishes to you
 
BlondEgg said:
Do you know if the other parts (i) (ii) (iii) (iv) are good?
What do you think? There comes a time when you need to troubleshoot your own work. Look at your answers and try to prove them wrong. If you can't, then they are probably correct.

For example, in (i) when you integrated did you get 1 or did you not?
In (ii), is you answer the magnitude-squared of what you got in (i) or is it not?

And so on.
 
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My attempt: Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE. PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##. PE of part in the tube = ##\frac{m}{l}(l - h)gh##. Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##. Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...

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