The Dirac equation in orthogonal coordinate systems. I. The local representation

He–McKellar–Wilkens-type effect, quantum holonomies and Aharonov–Bohm-type effect for bound states from the Lorentz symmetry breaking effects

“…∂x ν , and a unitary transformation on the wave function ψ (x) = U ψ ′ (x) [31][32][33]. Thereby, the Dirac equation (1) can be written in any orthogonal system in the following form:…”

On noninertial effects inducing a confinement of a neutral particle to a hard-wall confining potential

“…Since the operatorsĴ = − ∂ 1 , andˆ = − ∂ commute 1 It has been shown in Ref. [52] that the -component of the total angular momentum in cylindrical coordinates is given byĴ = − ∂ , where the eigenvalues are µ = ± 1…”

“…Thus, we can write σ 3 φ = ±φ = φ . We also have that the operatorsĴ = − ∂ [52], andˆ = − ∂ commute with the Hamiltonian of the right-hand side of (29), thus, we can take the solutions of (29) in the form:…”

A comment on the analogous confinement of a neutral particle to a quantum dot via noninertial effects

“…Moreover, we can observe that the Hamiltonian given in the right-hand-side of Eq. (7) commutes with the operatorsˆ = − ∂ ∂ , and J = − ∂ ∂ [50]. Hence, the solutions of the equation (7) are given in the form:…”

“…By observing that the line element (1) is valid only for values of the radial coordinate inside the range 0 < ρ < 1 ω , we have that the condition of making the confluent hypergeometric series to be a polynomial of 1 It has been shown in Ref. [50] that the -component of the total angular momentum in cylindrical coordinates is given byĴ = − ∂ , where the eigenvalues are…”