Quantum Loops: Solving the Particle-in-Potential Problem

[Klaus_Hoffmann]

Let be a classical particle with Hamiltonian

\pi _{t}-p^{2}-V(x)=0

can we describe the QM version of it (particle under the influence of a potential) using 'Loops' instead of Waves ?? i mean, although this is a toy model can we apply 'Quantum Loops' to solve the problem ??

 

[olgranpappy]

what are 'Quantum Loops'?

 

[Demystifier]

You mean something like loop quantum gravity?

 

[Klaus_Hoffmann]

Yes Demystifier..like 'Loop Quantum Gravity' but applied to normal QM (Non-relativistic) using Loops instead of Wave functions and so on

 

[Demystifier]

I have seen one paper claiming that when LQG type of quantization is applied to the ordinary harmonic oscillator, one does not recover the usual results on quantum harmonic oscillator. Unfortunately, I cannot recall which paper was that.

I would suggest to ask the same question at the "Beyond the Standard Model" subforum (or that moderators translate this thread there) because there are several LQG experts on this subforum.