Related papers: Quaternionic quantum particles
We compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. This analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations…
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
Learning probability distribution is an essential framework in classical learning theory. As a counterpart, quantum state learning has spurred the exploration of quantum machine learning theory. However, as dimensionality increases,…
In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of…
Scattering discussion due to Double Dirac Equation in Quaternionic version of relativistic quantum mechanics has been studied in this paper in details. In such a quantum mechanics Dirac equation in presence vector and scalar potential has…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
We introduce the concept of strong quantum speedup. We prove that approximating the ground state energy of an instance of the time-independent Schr\"odinger equation, with $d$ degrees of freedom, $d$ large, enjoys strong exponential quantum…
Quantum systems have an exponentially large degree of freedom in the number of particles and hence provide a rich dynamics that could not be simulated on conventional computers. Quantum reservoir computing is an approach to use such a…
Based on the dispersion chain of the Vlasov equations, the paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The proposed approach can be applied to consideration of classical and…
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex…
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…
We describe a quantum particle constrained on a catenoid, employing an effective description of quantum mechanics based on expected values of observables and quantum dispersions. We obtain semiclassical trajectories for particles,…
The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling…