Related papers: The Hartree functional in a double well
Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $\omega$ and the difference of the minima is close to a multiple of $\hbar \omega$. A WKB wave function is constructed…
The double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely WKB or instanton calculations. All these methods are…
We investigate a Hamiltonian with radial potential wells and an Aharonov-Bohm vector potential with two poles. Assuming that the potential wells are symmetric, we derive the semi-classical asymptotics of the splitting between the ground and…
We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to infinity. Two single-particle orbitals (one for each well)…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
A prime example of quantum tunnelling is the semiclassical 'energy splitting' of the levels of a symmetrical double well potential, or equivalently the flipping rate of an instanton. Curiously the accepted expression for the ground state…
The structure of the energy levels in a deep triple well is analyzed using simple quantum mechanical considerations. The resultant spectra of the first three energy levels are found to be composed of a ground state localized at the central…
The quantum dynamics of a few bosons in a double well potential is studied using a Bose Hubbard model. We consider both signs for the on-site interparticle interaction and also investigated the situations where they are large and small.…
We investigate quantum tunneling of two repulsive bosons in a triple-well potential subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic analysis, we evidence a far-resonant strongly-interacting regime…
We have prepared two ultracold fermionic atoms in an isolated double-well potential and obtained full control over the quantum state of this system. In particular, we can independently control the interaction strength between the particles,…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…
An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the…
We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonic trapping potential with a tunable zero-ranged barrier at the trap centre. The full characterisation of the ground state is done by calculating the…
We study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. We begin with the simplest case with no electron-electron interactions and find that besides the expected level splitting, bound states…
In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic lattice. The two wells of the Hamiltonian are prescribed by two rank-one connected martensitic twins, respectively. By constraining the deformed configurations to…
We consider the one-dimensional Schr\"{o}dinger operator in the semiclassical regime assuming that its double-well potential is the sum of a finite "physically given" well and a square shape probing well whose width or depth can be varied…
Motivated by our earlier argument that the apparent large cosmological constant from quantum fluctuations is actually an artifact of not using a full quantum mechanical superposition to determine the ground state in which the universe lives…
The solution to a problem in quantum mechanics is generally a linear superposition of states. The solutions for double well potentials epitomize this property, and go even further than this: they can often be described by an effective model…
The states of a boson pair in a one-dimensional double-well potential are investigated. Properties of the ground and lowest excited states of this system are studied, including the two-particle wavefunction, momentum pair distribution and…