Quantum Problem: Particle Motion Under Constraints and Christoffel Symbols

[tpm]

My question is if the QM problem of a classical particle under a potential V(x) so $$H=p^{2} +V(x)$$

Is the same of this problem of a particle constrained to move under a surface with the additional condition $$V(x)=0$$

Or a particle moving on a surface with $$\Gamma ^{i}_{jk}$$

So the potential is obtained from the 'Christoffel-Symbols'.

This problem is similar to the classic one by Einstein,.. where for 'weak field' you obtain Newton equation for the Potential..then my problem is if you can apply the same to QM

 

[Mentz114]

Hi tpm. You seem to jumping between theories too freely. The description in quantum terms of the bound particle is very different from the classical or GR scenario. They are not related in the way you imply. Have you studied QM ? There are no classical 'paths' or 'positions' in standard QM, and only probablities can be calculated.