What Angular Momentum Quantum Number Ensures Bound States?

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Homework Help Overview

The discussion revolves around identifying the angular momentum quantum number \( l_0 \) that ensures bound states for a given potential \( V = \frac{C}{r^3} - \frac{D}{r^2} \), where \( C \) and \( D \) are positive constants. The original poster expresses uncertainty about how to approach the problem, particularly in relating the quantum number to the effective potential.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants inquire about the effective potential and the form of the radial equation, suggesting a need for clarification on these concepts. The original poster questions whether they need to derive a relationship between the radius and the quantum number.

Discussion Status

The discussion includes attempts to clarify the problem's requirements, with some participants providing resources that may assist in understanding the topic. There is no explicit consensus on the approach to take, but a few directions have been suggested.

Contextual Notes

The original poster notes a lack of provided equations and expresses difficulty in finding relevant information online, indicating potential constraints in resources or guidance available for this problem.

kcasali
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Homework Statement


Remembering that a bound state exists if the effective potential is negative, find an angular momentum quantum number l0 such taht for all l<l0 the states are bound.

The given potential is V=(C/r3)-(D/r2), where C and D are positive numbers.

Homework Equations





The Attempt at a Solution



I don't even know where to start. I've been looking online for a few hours, I can't find anything even remotely helpful. Would I have to find an equation relating the radius to the quantum number, or am I way off track?
 
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What's the effective potential equal to ? How does the radial equation look like ?
 
dextercioby said:
What's the effective potential equal to ? How does the radial equation look like ?

I don't know if you're asking me if he gave any other equations (no, he didn't), or telling me I need those equations, haha.
 
Nevermind, I found it. Thank you. :)
 
I think this PowerPoint might help you. Good luck!

physics.wku.edu/~womble/phys480/lecture7.ppt
 

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