How to quantize a system in cubic well

[jianli]

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.

 

[vanesch]

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.

 

[David]

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.

 

[jianli]

Thanks to Vanesch and David. I'll try it.