Spherical well potential problem

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Homework Help Overview

The discussion revolves around a quantum mechanics problem involving a particle in a spherical well potential, defined by a negative potential value within a certain radius and an infinite potential beyond that radius. Participants are exploring how to approach the problem of finding energy levels and the radial wave function for specific states.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the method of solving the problem by treating different regions of the potential separately and then combining the solutions. There is a question about the appropriateness of setting the potential to zero in certain regions and concerns about the clarity of the problem statement.

Discussion Status

The discussion is active, with participants sharing their interpretations and approaches. Some guidance has been offered regarding the method of solving the problem, but there is still uncertainty about the combination of solutions from different potential regions.

Contextual Notes

Participants are navigating the complexities of combining solutions from different potential regions, and there is a mention of a potential misunderstanding in the problem's phrasing. The original problem constraints and definitions are under scrutiny.

xinoki
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Homework Statement



particle in a spherical well potential where V(r)= -V0 for 0<r<a and infinite for r>a


Homework Equations





The Attempt at a Solution


can i simply solve the problem for V0 treating the region r>a as zero and then solve 0<r<a treating V0=0 with the infinite potential for r>a and then stitch them together to obtain the wave function and energy
 
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It seems a bit strange to set the potential to a non-zero value inside the well if the potential outside is infinite. I get the feeling something's getting lost in your paraphrasing of the problem. Can you state the problem as it was given to you?
 
the problem was stated as above. find energy levels and radial wave function for the s states (l=0). i know how to solve each component individually (with V=-V0 or V= infinite). its the combination of the two that confuses me. I mentioned the above attempt because I've seen another solution where the solution was combined from a harmonic oscillator potential with the infinite potential well solution.
 
To answer your original question, yes, that's how you'd solve this problem.
 

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