Related papers: Self-adjoint extension procedure for a singular oscillator

Self-adjoint extension procedure for a singular oscillator

URL: http://arxiv.org/abs/2406.12927v1
Date: Fri, 14 Jun 2024 21:21:38 GMT
Title: Self-adjoint extension procedure for a singular oscillator
Authors: Anzor Khelashvili, Teimuraz Nadareishvili,
Abstract summary: It is shown that the self-adjoint extension violates the well-known property of equidistance of energy levels. The concept of quantum defect is generally introduced, and the wave function of the problem is written as a single function.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: For a singular oscillator, the Schrodinger equation is obtained an equation of eigenvalues, and the dependence of energy on the self-adjoint extension parameter is established. It is shown that the self-adjoint extension violates the well-known property of equidistance of energy levels for the oscillatory potential, well-known in quantum mechanics. The concept of quantum defect is generally introduced, and the wave function of the problem is written as a single function.

Related papers

Hysteresis and Self-Oscillations in an Artificial Memristive Quantum Neuron [79.16635054977068]
We study an artificial neuron circuit containing a quantum memristor in the presence of relaxation and dephasing. We demonstrate that this physical principle enables hysteretic behavior of the current-voltage characteristics of the quantum device.
arXiv Detail & Related papers (2024-05-01T16:47:23Z)
Quantum Principle of Least Action in Dynamic Theories With Higher Derivatives [44.99833362998488]
This form is the initial point for the construction of quantum theory. The correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit.
arXiv Detail & Related papers (2024-04-15T09:29:58Z)
Quantum model of hydrogen-like atoms in hilbert space by introducing the creation and annihilation operators [0.0]
An analytical approach with series is extensively used based on wave mechanics theory in most of quantum textbooks. We will illustrate how systematically making an appropriate groundwork to discover the coherent states can lead to providing the energy quantization and normalized radial wave functions attached to the matrix representation.
arXiv Detail & Related papers (2023-08-25T14:42:55Z)
Free expansion of a Gaussian wavepacket using operator manipulations [77.34726150561087]
The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes. We provide an alternative way to calculate the free expansion by recognizing that the Gaussian wavepacket can be thought of as the ground state of a harmonic oscillator. As quantum instruction evolves to include more quantum information science applications, reworking this well known problem using a squeezing formalism will help students develop intuition for how squeezed states are used in quantum sensing.
arXiv Detail & Related papers (2023-04-28T19:20:52Z)
An application of the HeunB function [0.0]
How does the inclusion of the gravitational potential alter an otherwise exact quantum mechanical result? The Schrodinger equation for the reduced mass is then solved to obtain the parabolic cylinder functions as eigenfunctions and the eigenvalues of the reduced Hamiltonian are calculated exactly. The eigenvalues are the determined from a recent series expansion in terms of the Hermite functions for the solution of the differential equation whose exact solution is the aforesaid HeunB function.
arXiv Detail & Related papers (2022-12-17T17:04:49Z)
Formulation of general dynamical invariants and their unitary relations for time-dependent coupled quantum oscillators [0.0]
An exact invariant operator of time-dependent coupled oscillators is derived using the Liouville-von Neumann equation. The unitary relation between this invariant and the invariant of two uncoupled simple harmonic oscillators is represented.
arXiv Detail & Related papers (2022-10-14T06:10:42Z)
Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator [0.0]
We study the time-dependent behaviour of quantum correlations of a system governed by out-of-equilibrium dynamics. Next, we study a specific case, where the system exhibits chaotic behaviour by computing the quantum Lyapunov from the time-dependent behaviour of OTOC.
arXiv Detail & Related papers (2022-10-03T18:00:02Z)
Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall. We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
arXiv Detail & Related papers (2022-09-12T08:21:12Z)
Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z)
Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)
Nonstationary deformed singular oscillator: quantum invariants and the factorization method [0.0]
New families of time-dependent potentials related with the stationary singular oscillator are introduced. Some special limits are discussed such that the singular barrier of the potential vanishes, leading to non-singular time-dependent potentials.
arXiv Detail & Related papers (2020-01-19T03:31:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.