What Happens to Energy Levels in a Reduced Potential Well?

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Homework Help Overview

The discussion revolves around the effects of reducing the potential energy in a quantum mechanical potential well, specifically concerning the ground state and first excited state of a particle. Participants explore the implications of this change on the wave functions and energy levels of the states involved.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question how a significant reduction in potential energy affects the bound states of a particle, particularly whether the ground state remains unchanged while the first excited state may become unbound. There is also discussion about the continuity of the wave function and its oscillatory nature in this new context.

Discussion Status

The conversation is ongoing, with participants expressing uncertainty about their ideas and seeking clarification on the relationship between potential energy and wave functions. Some guidance has been offered regarding the nature of potential shifts, but multiple interpretations of the effects on energy states are being explored.

Contextual Notes

Participants note that the topic is not extensively covered in their existing literature, indicating a potential gap in resources regarding the specific scenario being discussed.

indie452
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if V is reduced to much smaller than the zero point energy then what happens to the ground state and first excited state?


for this i know that the function becomes continuous and that the particle is unbound. does this mean that the function will also just have an oscillatory form?
 
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What are you asking exactly? you should know that shifting of potential V with a constant value Vo does not change the wavefunction.
 
yeah but if you change V from it being originally greater than E to being much smaller than the zero point energy surely this would change the ground and first excited wave function? wouldn't the fact that the E of the function is greater than V mean that it is no longer bound by the potential well?

i have these ideas but I am not sure if they are right and unfortunately this is not looked at in any of the books I've read.
 
so after thinking on it believe the ground state would stay the same as is the zero point energy which doesn't change, but then would the 1st excited state have enough energy to become unbound from the potential well
 

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