Free expansion of a Gaussian wavepacket using operator manipulations
- URL: http://arxiv.org/abs/2305.00059v1
- Date: Fri, 28 Apr 2023 19:20:52 GMT
- Title: Free expansion of a Gaussian wavepacket using operator manipulations
- Authors: Alessandro M. Orjuela and J. K. Freericks
- Abstract summary: 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.
- Score: 77.34726150561087
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The free expansion of a Gaussian wavepacket is a problem commonly discussed
in undergraduate quantum classes by directly solving the time-dependent
Schrodinger equation as a differential equation. In this work, 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 with its frequency adjusted to give the initial width of the
Gaussian, and the time evolution, given by the free-particle Hamiltonian, being
the same as the application of a time-dependent squeezing operator to the
harmonic oscillator ground state. Operator manipulations alone (including the
Hadamard lemma and the exponential disentangling identity) then allow us to
directly solve the problem. 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.
Related papers
- Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential [0.0]
The Schr"odinger equation is a fundamental equation in quantum mechanics.
Over the past decade, theoretical studies have focused on adapting the Dunkl derivative to quantum mechanical problems.
arXiv Detail & Related papers (2024-08-04T13:11:52Z) - 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) - Evolution of the wave-function's shape in a time-dependent harmonic
potential [0.0]
We show how to extract the effective dynamics for wave-packets evolving according to the Schrodinger equation.
We then show how to integrate the evolution of all the higher moments for a general wave-function in a time-dependent harmonic potential.
arXiv Detail & Related papers (2023-05-05T21:05:36Z) - Quantum Uncertainty as an Intrinsic Clock [0.0]
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom.
We show that the Ermakov-Lewis invariant for the classical evolution in a time-dependent harmonic potential is actually the quantum uncertainty of a Gaussian wave-packet.
This naturally extends the classical Ermakov-Lewis invariant to a constant of motion for quantum systems following Schrodinger equation.
arXiv Detail & Related papers (2022-12-19T13:32:55Z) - 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) - Numerical investigation of the logarithmic Schr\"odinger model of
quantum decoherence [0.0]
We present a model of collisional decoherence of the wavefunction of a quantum particle in position-space.
The validity of the logarithmic Schr"odinger equation has not yet been investigated numerically for general initial conditions.
arXiv Detail & Related papers (2021-10-11T03:18:03Z) - Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor.
We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
arXiv Detail & Related papers (2021-01-21T22:18:49Z) - Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered.
Operators of the form $hatcal H=hatA+ihatB$ are described.
Rigorous analytical analysis is performed for both wave and Green's functions.
arXiv Detail & Related papers (2020-10-13T15:50:49Z) - Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit.
We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront.
The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
arXiv Detail & Related papers (2020-03-09T21:27:02Z) - Operator-algebraic renormalization and wavelets [62.997667081978825]
We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory.
A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
arXiv Detail & Related papers (2020-02-04T18:04:51Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.