Say we have a free quantum mechanical particle constrained to move on the surface of S^6;(adsbygoogle = window.adsbygoogle || []).push({});

x1^2 + x2^2 + x3^2 + x4^2 + x5^2 + x6^2 + x7^2 = R^2

Can we add a simple potential such that for low energies the particle is "constrained" to move in some sub space of S^6, say S^3, but for higher energies the particle has "full access" of the space S^6.

What might be such a simple potential?

Does this potential have a topology?

Is their a group represented by the quantum mechanics of a free particle constrained to move on the surface S^3?

Thanks for your help.

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# Q.M. on S^6, add potential gives Q.M. on S^3?

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