Related papers: Virtual states in the coupled-channel problems wit…
The Schr\"odinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order…
Through numerical examples we show that the complex scaling method is suited to explore the pole structure in multichannel scattering problems. All poles lying on the multisheeted Riemann energy surface, including shadow poles, can be…
In this paper we introduce a new method for the simulation of a weak solution of the Schr\"odinger-type equation where the potential is piecewise constant and positive. The method, called killing walk on spheres algorithm, combines the…
A practical method to solve cut-off Coulomb problems of two-cluster systems in the momentum space is given. When a sharply cut-off Coulomb force with a cut-off radius $\rho$ is introduced at the level of constituent particles, two-cluster…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
The complex scaling method (CSM) is one of the most powerful methods of describing the resonances with complex energy eigenstates, based on non-Hermitian quantum mechanics. We present the basic application of CSM to the properties of the…
Recent demonstrations of superconducting quantum computers by Google and IBM and trapped-ion computers from IonQ fueled new research in quantum algorithms, compilation into quantum circuits, and empirical algorithmics. While online access…
Rigorous quantum dynamics calculations provide essential insights into complex scattering phenomena across atomic and molecular physics, chemical reaction dynamics, and astrochemistry. However, the application of the gold-standard quantum…
This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schr\"odinger…
Quantum simulators offer the potential to utilize the quantum nature of a physical system to study another physical system. In contrast to conventional simulation, which experiences an exponential increase in computational complexity,…
Variational optimization of neural-network representations of quantum states has been successfully applied to solve interacting fermionic problems. Despite rapid developments, significant scalability challenges arise when considering…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
Deep in the ultrastrong light-matter coupling regime, it has been predicted that the ground state of a two-level atom interacting with a cavity mode takes the form of a "virtual" Schr\"odinger cat entangled state between light and matter.…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of 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…
Classical simulations of quantum computations are vital for the future development of this emerging technology. To this end, decision diagrams have been proposed as a complementary technique which frequently allows to tackle the inherent…
Solving for the bound state eigenvalues of the Schr\"odinger equation is a tedious iterative process when the conventional shooting or matching method is used. In this work, we bypass the eigenvalue's dependence on the eigenfunction by…
The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from…
We present a method for efficiently finding solutions of L\"uscher's quantisation condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such…