How to quantize a system in cubic well

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    Cubic System
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Discussion Overview

The discussion revolves around the quantization of a cubic potential well, specifically in the context of superconducting qubits based on current-biased Josephson junctions. Participants explore the theoretical framework for quantizing the system and the implications for the energy states involved.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the method for quantizing a cubic well, seeking hints or suggestions.
  • Another participant suggests that separation of variables might lead to treating the cubic well as three one-dimensional wells.
  • A different participant confirms that separation of variables is indeed applicable and notes the importance of careful counting of modes and degeneracies, mentioning that a truly cubic well would have three degenerate modes for the first excited state.

Areas of Agreement / Disagreement

Participants generally agree on the applicability of separation of variables for quantizing the cubic well, but there are nuances regarding the counting of modes and degeneracies that remain to be fully clarified.

Contextual Notes

There may be limitations in the assumptions regarding the cubic nature of the well and the implications for mode counting and degeneracies that have not been fully explored.

jianli
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Hi, all,
I'm studying the superconducting qubit based on current-biased josephson junction. The system can be considered as a particle in a washboard well, or a cubic well. The two states |0> and |1> are the ground and the first excited ones. But How to quantize the cubic well.
Could anyone give me some hint or suggestion?
Thanks.
 
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jianli said:
But How to quantize the cubic well.
Could anyone give me some hint or suggestion?
Thanks.

I would naively think that separation of variables gives you 3 times a one-dimensional well, no ?

cheers,
Patrick.
 
It will indeed separate so then you just have to be careful about counting modes, etc. and degeneracies. If it is truly cubic (the lengths of each side are the same), then there there are 3 degenerate modes for the first excited state.
 
Thanks to Vanesch and David. I'll try it.
 

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