Related papers: Wave Function Identity: A New Symmetry for 2-elect…
We solve the stationary Schr\"odinger equation for a particle confined to a 3D spherical wedge -- the region $\{(r,\theta,\phi): 0 \leq r \leq R,\, 0 \leq \theta \leq \pi,\, 0 \leq \phi \leq \Phi\}$ with Dirichlet BCs on all surfaces. This…
We present a procedure to solve the Schroedinger equation of two interacting electrons in a quantum dot in the presence of an external magnetic field within the context of quasi-exactly-solvable spectral problems. We show that the…
We propose three core ideas: 1. the wave-particle duality of the qudit quantum space; 2. the classification of all elementary quantum gates by ordered pairs of qudit functionals; 3. a new type of quantum gates called the "quantum wave…
Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schr\"{o}dinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives…
Spontaneous collapse models use non-linear stochastic modifications of the Schroedinger equation to suppress superpositions of eigenstates of the measured observable and drive the state to an eigenstate. It was recently demonstrated that…
The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in Hartree-Fock theory, where the uniform paramagnetic state of…
New quantum phenomena are continuously being discovered in 2D systems. In particular, the charge density wave (CDW) has the aspect of a quantum crystal with a macroscopic wave function (order parameter), so unlike quantum liquids…
A thermally isolated quantum system undergoes unitary evolution by interacting with an external work source. The two-point energy measurement (TPM) protocol defines the work exchanged between the system and the work source by performing…
We have investigated the wave-function feature of Rydberg sodium in a uniform electric field and found that the core-induced interaction of non-hydrogenic atom in electric field can be directly visualized in the wave-function. As is well…
The spin susceptibility of a two-dimensional electron system is calculated by determining the spin-polarization dependence of the ground-state energy within the self-consistent mean-field theory of Singwi et al. (STLS). Results are…
In this paper we solve the one-particle Schr\"{o}dinger equation in a magnetic field whose flux lines exhibit mutual linking. To make this problem analytically tractable, we consider a high-symmetry situation where the particle moves in a…
We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the…
The Schr\"odinger's wave function can naturally be realized as an 'instantaneous resonant spatial mode' in which quantum particle moves and hence the Born's rule is derived after identifying its origin. This realization facilitates the…
Artificial molecular states of double quantum dots defined in bilayer graphene are studied with the atomistic tight-binding and its low-energy continuum approximation. We indicate that the extended electron wave functions have opposite…
We study the numerical solution of the non-relativistic Schr\"{o}dinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the…
In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a…
We study two-electron states confined in two coupled quantum dots formed by a short-range potential in a two-dimensional topological insulator. It is shown that there is a fairly wide range of the system parameters, where the ground state…
The self-dual condition, which ensures invariance under electromagnetic duality, manifests as a partial differential equation in nonlinear electromagnetism theories. The general solution to this equation is expressed in terms of an…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
Soft-operators, loosely speaking, are operators which create or annihilate zero energy massless particles on the celestial sphere in Minkowski space. The Lorentz group acts on the celestial sphere by conformal transformation and the…