Quantum Loops: Solving the Particle-in-Potential Problem

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In summary, the conversation discusses the possibility of using 'Quantum Loops' instead of wave functions to describe a classical particle with Hamiltonian under the influence of a potential. It also mentions the application of loop quantum gravity to solve this problem and the potential limitations of this approach. It is suggested to ask the question in a forum with LQG experts for further discussion on the topic.
  • #1
Klaus_Hoffmann
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Let be a classical particle with Hamiltonian

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

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 ??
 
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  • #2
what are 'Quantum Loops'?
 
  • #3
You mean something like loop quantum gravity?
 
  • #4
Yes Demystifier..like 'Loop Quantum Gravity' but applied to normal QM (Non-relativistic) using Loops instead of Wave functions and so on
 
  • #5
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.
 
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1. What is the Particle-in-Potential Problem?

The Particle-in-Potential Problem is a fundamental problem in quantum mechanics that involves finding the energy levels and wavefunctions of a particle in a given potential.

2. How are Quantum Loops used to solve this problem?

Quantum Loops are a mathematical tool used in quantum mechanics to represent the particle's motion in a potential. These loops are used to calculate the energy levels and wavefunctions of the particle.

3. What makes Quantum Loops a powerful method for solving the Particle-in-Potential Problem?

Quantum Loops are powerful because they allow for the calculation of energy levels and wavefunctions for any type of potential, including complex potentials that cannot be solved analytically.

4. Are there any limitations to the use of Quantum Loops?

Yes, Quantum Loops are limited to one-dimensional potentials and do not take into account the effects of spin or interactions with other particles.

5. How do the results obtained from Quantum Loops compare to other methods of solving the Particle-in-Potential Problem?

The results obtained from Quantum Loops are comparable to other methods such as the Schrödinger equation, but they can be obtained more efficiently and accurately for certain types of potentials.

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