Related papers: The Step-Harmonic Potential
We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly…
We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one and quasi-two-dimensional…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and…
One of the best systems for the study of quantum chaos is the atomic nucleus. A confined particle with general boundary conditions can present chaos and the eigenvalue problem can exhibit this fact. We study a toy model in which the…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…
By using an exact solution to the time-dependent Schr\"{o}dinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source…
We give a study of some molecular vibration potentials by solving the D-dimensional Schrodinger equation using the asymptotic iteration method (AIM). The eigenvalue values obtained by the AIM are found to agree with analytic solutions. The…
Employing the phase-space representation of second order ordinary differential equations we developed a method to find the eigenvalues and eigenfunctions of the 1-dimensional time independent Schr\"odinger equation for quantum model…
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…
Schr\"odinger-type eigenvalue problems are ubiquitous in theoretical physics, with quantum-mechanical applications typically confined to cases for which the eigenfunctions are required to be normalizable on the real axis. However, seeking…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that…
We study the application of the coherent-state path integral as a numerical tool for wave-packet propagation. The numerical evaluation of path integrals is reduced to a matrix-vector multiplication scheme. Together with a split-operator…
We study evolution of a quantum particle in a harmonic potential whose position and momentum are repeatedly monitored. A back-action of measuring devices is accounted for. Our model utilizes a generalized measurement corresponding to the…
We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…