Quantum virial and confinement

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SUMMARY

The discussion centers on the quantum virial and the confinement of particles as they pass through a slit. It is established that the virial represents the kinetic energy component associated with a specific spatial dimension. When a particle is confined, such as when passing through a slit, its energy spectrum becomes discretized, particularly in the lateral dimension. This discretization is crucial for explaining the fringe patterns observed in experiments involving particles, such as the one-slit experiment.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the concept of the virial in kinetic energy
  • Knowledge of particle confinement and energy discretization
  • Basic grasp of experimental setups like the one-slit experiment
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  • Research the implications of quantum confinement on particle behavior
  • Study the mathematical formulation of the virial theorem in quantum mechanics
  • Explore the phenomenon of wave-particle duality in quantum experiments
  • Investigate the role of energy discretization in quantum systems
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Physicists, quantum mechanics students, and researchers interested in particle behavior and experimental quantum physics.

DaTario
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Hi All

As far as I know, the virial is the component of the Kinetic energy associated with one particular spatial dimension.

Aditionally, when a particle is confined, its energy spectrum gets discretized.

So my question:
if, in three dimensions, a particle with momentum in ^i passes a slit in a plane (^j and ^k with the slit along ^k), as long the particle is inside the slit, laterally it is confined in the dimension ^j, so is it correct to state that the energy associated with v_j is discretized?

Thank you

DaTario
 
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No. But in fact I still believe that it is possible to describe the one slit experiment with tiny particles using the fact that when the particle crosses the slit, during a small interval of time it is inside a well and its spectrum in the transverse direction gets discretized. It is, then, precisely this dicretization of energy that makes the particle arrive in fringes at the ecran. Additional hypothesis must be discussed, and questions must be answered, but I think it would provide a nice way to explain the fringe paterns.

Best Regards,
DaTario
 

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