What are the 3 challenging QM problems in FDR407?

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Homework Help Overview

The discussion revolves around three challenging quantum mechanics problems from a course identified as FDR407. Participants are sharing resources and insights related to these problems, particularly focusing on the finite square well and the hydrogen atom.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of Griffiths's textbook as a reference for understanding the finite square well problem, particularly the transcendental equation that arises from solving the Schrödinger equation. There are mentions of boundary conditions and the need to analyze function intersections graphically. Additionally, there is a question about the specific textbook being referenced.

Discussion Status

Some guidance has been provided regarding the finite square well problem, including the suggestion to plot functions to find intersections. Participants are exploring different aspects of the problems without reaching a consensus on solutions.

Contextual Notes

There is a note that the textbook provides even solutions, while the participants need to focus on odd solutions, indicating a specific constraint in their approach to the problems.

eit32
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3 Problems that i am struggling with are attached. FDR407
 

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here it is as a PDF
 

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The only help I'll give here is for #2, for which I'm using Griffiths's excellent QM book (Chapter 2) as a reference. If you can get your hands on that book, buy it!

When you analyze the finite square well, after solving the Schrödinger equation, imposing boundary continuity conditions, and cleaning up the notation using a dummy variables "Z" and "Z0", you get an equation for Z that has tan(Z) on one side and sqrt{(Z0/Z)^2-1} on the other side. This can't be solved traditionally; the best you can do is plot both functions together and see where they intersect. That's why it's called a transcendental.

It looks like your teacher is giving you the hydrogen atom, since the mass of the electron is given, along with the traditional 1 angstrom distance from the nucleus.
 
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Note: Griffiths's text provides the even solutions, and you have to do the odd solutions, so your transcendental will be a bit different.
 
What is the full name of that Textbook that you guys talking about
 
"Introduction to Quantum Mechanics," David J. Griffiths, Prentrice Hall. Has a live cat on one cover and a dead cat on the other :)
 

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