Related papers: Factorization of the Quantum Fractional Oscillator
Momentum is analyzed as a random variable in stochastic quantum mechanics. Arbitrary potential energy functions are considered. The oscillator is presented as an example.
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
There is a widespread belief in the quantum physical community, and in textbooks used to teach Quantum Mechanics, that it is a difficult task to apply the time evolution operator Exp{-itH/h} on an initial wave function. That is to say,…
This is an introduction to the microscopic theories of the FQHE. After a brief description of experiments, trial wavefunctions and the physics they contain are discussed. This is followed by a description of the hamiltonian approach,…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
In a full solution for a scalar quantum field coupled to an accelerating isotropic universe, all constituent non-autonomous modes of elementary excitation cease to oscillate and become unstable at a discrete sequence of times. After…
We develop and analyze a new method for manipulation of energy in a quantum harmonic oscillator using coherent, e.g., electromagnetic, field and incoherent control. Coherent control is typically implemented by shaped laser pulse or tailored…
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the…
In this paper we study the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan. This system with position-dependent mass allows a natural quantization procedure and is shown to display shape invariance. Its energy…
The concept of energy-dependent forces in quantum mechanics is re-analysed. We suggest a simplification of their study via the representation of each self-adjoint and energy-dependent Hamiltonian H=H(E) with real spectrum by an auxiliary…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…
Fault tolerant quantum simulation via the phase estimation algorithm and qubitization has a T-gate count that scales proportionally to the 1-norm of the Hamiltonian, the cost of block encoding the Hamiltonian, and inversely proportionally…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
We study a quantum harmonic oscillator undergoing thermalization. To describe the thermalization process, we generalize the Ermakov-Lewis-Riesenfeld (ELR) invariant method for the oscillator. After imposing appropriate conditions on the…
Using a combination of semiclassical and recently developed wave packet propagation techniques we find the quantum self-ionization process of highly excited ions moving in magnetic fields which has its origin in the energy transfer from the…
The prevalent role of force in traditional quantum mechanics is outlined, with special reference to approximate calculations for stationary states. It will be explored how far this force concept can be made useful in the concerned area. The…
Quantum phase-space distributions (Wigner functions) for the plane rotator are defined using wave functions expressed in both angle and angular momentum representations, with emphasis on the quantum superposition between the Fourier dual…
Based on the Caputo definition of the fractional derivative the ground state spectra of mesons are classified as multiplets of the fractional rotation group. The comparison with the experimental values leads to the conclusion, that quarks…
Feynman's prescription for a quantum simulator was to find a hamitonian for a system that could serve as a computer. P\'olya and Hilbert conjecture was to demonstrate Riemann's hypothesis through the spectral decomposition of hermitian…