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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