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A general quantization rule for bound states of the Schrodinger equation is presented. Like fundamental theory of integral, our idea is mainly based on dividing the potential into many pieces, solving the Schr\"odinger equation, and…
In this paper, the application of quantum simulations and quantum machine learning to solve low-energy nuclear physics problems is explored. The use of quantum computing to deal with nuclear physics problems is, in general, in its infancy…
We find the most general spherically symmetric non singular black hole solution in a special class of teleparallel theory of gravitation. If $r$ is large enough, the general solution coincides with the Schwarzschild solution. Whereas, if…
I develop the solution to the problem of an electron confined in a composite quadratic well subject to a simple, external periodic force. The method of solution illustrates several of the basic techniques useful in formally solving the…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
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…
This article examines the suggestion made in Ref. [EPL, 115 (2016) 60001] that a solution to a particle in an infinite spherical well model, if it is square-integrable, is a physically valid solution, even if at the precise location of the…
The prosperous development of both hardware and algorithms for quantum computing (QC) potentially prompts a paradigm shift in scientific computing in various fields. As an increasingly active topic in QC, the variational quantum algorithm…
In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
In this article we present a study of the effects of hydrostatic pressure on the energy levels of a quantum dot with an electron. A quantum dot is modeled using an infinite potential well and a two-dimensional harmonic oscillator and solved…
The previously proposed Heisenberg-type relation $ E_c t_c >> \hbar {\cal C}$ for the energy used by a quantum computer, the total computation time and the logical ("classical") complexity of the problem is verified for the following…
Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness…
The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…
We give precise meaning to piecewise constant potentials in non-commutative quantum mechanics. In particular we discuss the infinite and finite non-commutative spherical well in two dimensions. Using this, bound-states and scattering can be…
Coupled asymmetric double well ($a\phi^2-b\phi^3+c\phi^4$) one-dimensional potentials arise in the context of first order phase transitions both in condensed matter physics and field theory. Here we provide an exhaustive set of exact…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…