A Non-Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

In standard quantum mechanics, the coupling between quantum systems is described by a potential interaction term in the Hamiltonian. This type of coupling is well-rooted in nature and shapes the universe around us, from the interactions between single photons to the attractive force between atoms that forms molecules. Quantum mechanics does not forbid other kinds of interactions to take place. In this paper, a non-standard quantum coupling between quantum systems is proposed, originated from the kinetic energy rather than the potential interaction in the Hamiltonian. Unlike the potential-based coupling, the proposed coupling changes the fundamental structure of quantum mechanics in the form of modified uncertainty relations that are shaped by the coupling between the particles in the system. Two prototypical examples of non-standard systems that perform such kinetic-based coupling are presented. In the first example, it considers a particle confined in a heterostructure, such as a quantum dot, where the coupling is between the particle and dynamic walls that determine the size of the heterostructure. The second example involves a particle in a 3D heterostructure with coupling between its position axes. It then discusses several future implications of the proposed type of non-standard coupling.