Related papers: Quantum Bound States with Zero Binding Energy
On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive…
Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help…
For the quantised, massless, minimally coupled real scalar field in four-dimensional Minkowski space, we show (by an explicit construction) that weighted averages of the null-contracted stress-energy tensor along null geodesics are…
We expand on previous work involving "vacuum-bounded" states, i.e., states such that every measurement performed outside a specified interior region gives the same result as in the vacuum. We improve our previous techniques by removing the…
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a…
A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such…
We consider two kinds of superpositions of squeezed states of light. In the case of superpositions of first kind, the squeezing and all higher order squeezing vanishes. However, in the case of the second kind, it is possible to achieve a…
We show that any pure, two-mode, $N$-photon state with $N$ odd or equal to two can be transformed into an orthogonal state using only linear optics. According to a recently suggested definition of polarization degree, this implies that all…
Atomic-like systems in which electronic motion is two dimensional are now realizable as ``quantum dots''. In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular…
We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by…
We extend our previous analysis of the quantum state during and after $O(4)$-symmetric bubble nucleation to the case including gravitational effects. We find that there exists a simple relationship between the case with and without…
Quasiclassical solution of the three-dimensional Schredinger's equation is given. The existence of nonzero minimal angular momentum M_0 = \hbar /2 is shown, which corresponds to the quantum fluctuations of the angular momentum and…
Energy densities of the quantum states that are superposition of two multi-electron-positron states are examined. It is shown that the energy densities can be negative only when two multi-particle states have the same number of electrons…
In this paper we establish the existence of bound state solutions of any given order to $$ \Delta_m u +f(u)=0, x\in R^N, N\ge m>1, (P) $$ where $\Delta_m u=\nabla\cdot(|\nabla u|^{m-2}\nabla u)$ using the same techniques as in [GST] to…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
The D -dimensional quasi - exact solutions for the singular even - power anharmonic potential $V(q)=aq^2+bq^{-4}+cq^{-6}$ are reported. We show that whilst Dong and Ma's [5] quasi - exact ground - state solution (in D=2) is beyond doubt,…
$D$-dimensional Schr\"{o}dinger equation is addressed for square root power law potential. Bound state unnormalized eigenfunctions and the energy eigenvalues are obtained using wave function ansatz method. Some special cases are studied at…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
It has been stated that for a short-ranged surface interaction, the probability of a low-energy particle sticking to a surface always vanishes as $s\sim k$ with $k\to 0$ where $k=\sqrt{E}$. Deviations from this so-called universal threshold…
In the framework of non-relativistic quantum mechanics and with the help of the Greens functions formalism we study the behavior of weakly bound states as they approach the continuum threshold. Through estimating the Green's function for…