How does the potential for Quantum Mechanics differ between two scenarios?

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Homework Help Overview

The discussion revolves around the differences in potential energy scenarios in quantum mechanics, specifically comparing two potential functions in the context of Schrödinger's equation, wave functions, and energy states.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore how to treat infinite potentials in one-dimensional Schrödinger's equation and question the implications of boundary conditions associated with infinite potential scenarios.

Discussion Status

Some participants are clarifying their understanding of how infinite potentials affect the treatment of Schrödinger's equation, while others are attempting to connect their knowledge of boundary conditions to the specific cases presented. There is an indication of progress as one participant expresses confidence in their understanding.

Contextual Notes

One participant notes a technical issue with posting mathematical expressions, which may affect the clarity of the discussion.

ynuo
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How does this potential:

V(x)={Inf for x<0, bx for 0<x<a, Inf for x>a}

differ from:

V(x)={Inf for x<0, bx for x>0}

with regards to Schrödinger's equation, wave functions, and the energy states.

P.S. the tex graphics are not showing when I try to post my question using tex macros. This is why I resorted to plain ascii.
 
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Do you know how to treat an infinite potential within the context of 1-dim SE ?
 
This is the part that I have trouble with. I know that if I had a constant
potential or any other type of potential, then a substitution in Schrödinger's
equation will be required. From there I will have to solve a DE. But in
the case of infinite potential I am not sure.
 
Saying 'infinite potential' specifies a boundary condition for the DE. Guess which one?
 
I think I got it. Thanks.
 

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