Related papers: Constructing Hermitian Hamiltonians for spin zero …
When a two-dimensional curved surface is conceived as a limiting case of a curved shell of equal thickness d, where the limit d\rightarrow0 is then taken, the well-known geometric potential is induced by the kinetic energy operator, in fact…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm)}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian ${\cal H}$ are…
Noncommutivity of position and momentum makes it difficult to formulate the unambiguous structure of the kinetic part of Hamiltonian for the position-dependent effective mass (PDEM). Various existing proposals of writing the viable kinetic…
Consider a homogenous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in…
Decompositing of $N+1$-dimensional gradient operator in terms of Gaussian normal coordinates $(\xi^{0},\xi^{\mu})$, ($\mu=1,2,3,...,N$) and making the canonical momentum $P_{0}$ along the normal direction $\mathbf{n}$ to be hermitian, we…
The diagonalization of the metrical and canonical Hamilton operators of a scalar field with an arbitrary coupling, with a curvature in N-dimensional homogeneous isotropic space is considered in this paper. The energy spectrum of the…
Active proteins and membrane-bound motors exert force dipole flows along fluid interfaces and lipid bilayers. We develop a Hamiltonian framework for the interactions of pusher and puller dipoles embedded in an incompressible two-dimensional…
It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of a charged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatially dependent, magnetic field in two spatial dimensions can be written as the anticommuator…
Inspired by the recent work of Filho et al., a Hermitian momentum operator is introduced in a general curved space with diagonal metric. The modified Hamiltonian associated with this new momentum is calculated and discussed. Furthermore,…
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\mu$ in such a theory transforms as a pseudovector…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results…
The Hermitian Cartesian quantum momentum operator $\mathbf{p}$ for an embedded surface $M$ in $R^{3}$ is proved to be a constant factor $-i\hbar $ times the mean curvature vector field $H\mathbf{n}$ added to the usual differential term.…
Within CPT-symmetric quantum mechanics the most elementary differential form of the charge operator C is assumed. A closed-form integrability of the related coupled differential self-consistency conditions and a natural embedding of the…
A non-Hermitian P$_{\phi}$T$_{\phi}$-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians H$_{r}$, H$_{\theta}$, and H$_{\phi}$ play essential roles and offer some user-feriendly…
We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics…
We give a new reduction of a general diatomic molecular Hamiltonian, without modifying it near the collision set of nuclei. The resulting effective Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator (the…
Recently, it was established that there exists a direct relation between the non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for non-Hermitian Hamiltonians-, and boundary zero modes for Hermitian topological…
Geometric momentum is the appropriate momentum for a particle constrained to move on a curved surface, which depends on the extrinsic curvature and leads to observable effects, and curvature-induced quantum potentials appear for a…