Quantized Kinetic Energy of Relativistic Objects

[jrvinayak]

Hello,

I want to know if energy added to moving objects is quantized. Kinetic energy of an moving object is given as KE = (γ - 1) mc² , where γ is 1/√(1-v²/c²).

And quantum theory talks about any energy always being quantized. So can the KE in moving objects be quantized?

 

[Dale]

Hi jrvinayak, welcome to PF!

And quantum theory talks about any energy always being quantized.

This is a very common misconception. Even in quantum mechanics there are some systems where energy is quantized and other systems where the energy is not quantized. One very interesting and simple system is the so-called finite potential well

https://en.wikipedia.org/wiki/Finite_potential_well

This system includes both bound states which are quantized and free states which are not quantized.

 

[pervect]

I agree with DaleSpam's response. I'd just add that less formally, the "potential well" problem is known as a "particle in a box". You might google for this term. The particle in a box has quantized momentum and energy, but the details depends on the size of the box. Formally, we'd describe this dependence by saying "it depends on the boundary conditions". The free particle that's not confined to a box doesn't have quantized momentum or energy levels. The best forum to ask for further details would be the quantum mechanics forum, it's not really within the scope of GR.

 

[vanhees71]

Be, however, warned that "particle in a box" often means the only apparently simpler problem of an infinitely high potential well. However, this is a particularly difficult case, if done mathematically correctly, because for this problem no proper momentum observable exists anymore, but that's a topic belonging more to the quantum-theory forum. The finite-potential well is only a bit more work but has the advantage of having a well-defined realization of the Heisenberg algebra in terms of the wave-mechanics formulation.