arXiv subjects

Techapon Kampu

Publications and source records attributed to Techapon Kampu.

2 recordsLinked to original sources

arXiv2026

Constructing the Hamiltonian for a free 1D KFGM particle in an interval

We analyze the problem of a free 1D Klein-Fock-Gordon-Majorana (KFGM) particle in an interval. By free, we mean that there is no potential within the interval and that its walls are penetrable; hence, the pertinent energy current density does not vanish at the walls. Certainly, quantization in an interval is not trivial because certain restrictions imposed by the domains of the operators involved arise. Here, our objective is to obtain the Hamiltonian for these particles. In practice, the Feshbach-Villars (FV)--free Hamiltonian is the proper operator for characterizing them and is a function of the momentum operator. Additionally, a Majorana condition must also be imposed on the wavefunctions on which these two operators can act. Thus, we start by calculating the pseudo self-adjoint momentum operator. A three-parameter set of boundary conditions (BCs) constitutes its domain. Up to this point, the domain of the Hamiltonian is induced by the domain of the momentum operator; however, we ensure that only the BCs for which the energy current density has the same value at each end of the interval are in its domain. All these BCs essentially belong to a one-parameter set of BCs. Moreover, because the FV equation is invariant under the operation of parity, the parity-transformed wavefunction is also a solution of this equation, which further restricts the domain of the free FV Hamiltonian. Finally, knowing the most general three-parameter set of BCs for the pseudo self-adjoint FV Hamiltonian for a 1D KFGM particle in an interval, we find that only two BCs can remain within the domain of the FV--free Hamiltonian: the periodic BC and the antiperiodic BC. These BCs are satisfied by both the two-component FV wavefunction, with these components being related, and the one-component KFG wavefunction, which can be real or imaginary.

quant-ph↗

arXiv2025

Nontrivial local observables and impermeable and permeable boundary conditions for 1D KFGM particles

Real solutions of the 1D Klein-Fock-Gordon (KFG) equation automatically cancel out the usual two-vector current density; consequently, the respective continuity equation is trivially satisfied, and a globally conserved quantity cannot be obtained. Additionally, distinguishing between impermeable and permeable boundary conditions (BCs) at a given point is not possible. We address these first-quantized conflicts by using the simplest nontrivial local observables, i.e., an energy density and an energy current density, which allows us to characterize a strictly neutral 1D KFG particle, i.e., a 1D KFG-Majorana (KFGM) particle, when it is confined to an interval and when it is restricted, e.g., in an interval with transparent walls. All the BCs for this system are extracted from the pseudo self-adjointness of the Feshbach-Villars (FV) Hamiltonian plus two Majorana conditions. We show that these energy densities are components of an unusual energy-momentum tensor and can satisfy a continuity equation, leading to a conserved quantity for all available BCs. Moreover, the energy current density can characterize all the BCs as either impermeable or permeable. In contrast, the commonly used energy current density -- a component of the usual energy-momentum tensor -- cannot characterize all the BCs. Additionally, this quantity and its respective energy density -- another component of the usual energy-momentum tensor -- may not lead to a conserved quantity. We also obtain the BCs for which the abovementioned densities and those commonly used are equally satisfactory. In fact, this occurs only for four impermeable BCs and a one-parameter set of permeable BCs. Our results highlight the important role played by the BCs when they are imposed on a system in which particles occupy a finite region.

quant-ph↗