Quantum virial and confinement

[DaTario]

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

 

[Greg Bernhardt]

@DaTario did you find any more insight on this topic?

 

[DaTario]

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