Related papers: Factorization of the Quantum Fractional Oscillator
A parametrically modulated oscillator has two opposite-phase vibrational states at half the modulation frequency. An extra force at the vibration frequency breaks the symmetry of the states. The effect can be extremely strong due to the…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain, and fractional order…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
We define a new quantum Hermitian operator (namely, the energy variance operator) which is simply duplicated from the statistical definition of energy variance in classical physics. Its expectation value yields the standard deviation of the…
Using a particular form of the quantum K-essence scalar field, we show that in the quantum formalism, a fractional differential equation in the scalar field variable, for some epochs in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) model…
Singular functions and, in general, H\"older functions represent conceptual models of nonlinear physical phenomena. The purpose of this survey is to demonstrate the applicability of fractional velocity as a tool to characterize Holder and…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…
Entanglement in high energy and and nuclear reactions is receiving great attention. A proper description of these reactions uses density matrices, and the express of entanglement in terms of {\it separability}. Quantum tomography bypasses…
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part…
A time fractional quantum framework has been introduced into quantum mechanics. A new version of the space-time fractional Schr\"odinger equation has been launched. The introduced space-time fractional Schr\"odinger equation has a new scale…
The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the…