Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Fermi Level Dynamics01:12

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Qubit-Efficient Quantum Chemistry with the ADAPT Variational Quantum Eigensolver and Double Unitary Downfolding.

Journal of chemical theory and computation·2025
Same author

Ballast Charges for Semiconductor Spin Qubits.

Physical review letters·2025
Same author

Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases.

Physical review. A·2024
Same author

Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer.

Chemical science·2023
Same author

Symmetry Breaking Slows Convergence of the ADAPT Variational Quantum Eigensolver.

Journal of chemical theory and computation·2022
Same author

Fermionic Many-Body Localization for Random and Quasiperiodic Systems in the Presence of Short- and Long-Range Interactions.

Physical review letters·2022
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: May 18, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Analytically solvable driven time-dependent two-level quantum systems.

Edwin Barnes1, S Das Sarma

  • 1Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Researchers developed a simple algorithm for unlimited analytical solutions to the time-dependent Schrödinger equation, crucial for quantum computing and physics. This method provides exact solutions for driven two-level systems, aiding qubit control.

More Related Videos

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Related Experiment Videos

Last Updated: May 18, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

  • Quantum Mechanics
  • Quantum Computing
  • Mathematical Physics

Background:

  • Analytical solutions for the time-dependent Schrödinger equation are rare but essential in physics.
  • Driven two-level systems are fundamental models in quantum mechanics and quantum information.
  • Exact solutions are critical for precise control and understanding of quantum systems.

Purpose of the Study:

  • To present a novel, simple algorithm for generating an unlimited number of exact analytical solutions.
  • To demonstrate the applicability of these solutions to driven two-level systems.
  • To provide new tools for qubit control in quantum computing.

Main Methods:

  • Developed a general method based on a single real function to define driving terms and evolution operators.
  • Established constraints (inequality and initial conditions) for the defining function.
  • Applied the method to derive new exact analytical solutions for the time-dependent Schrödinger equation.

Main Results:

  • An unlimited number of exact analytical solutions can be generated using the proposed algorithm.
  • A general single-axis driving term and its evolution operator are determined by a single constrained real function.
  • Several new exact analytical solutions were successfully derived and demonstrated.

Conclusions:

  • The presented algorithm offers a powerful and accessible way to find exact analytical solutions for driven two-level systems.
  • The method and derived solutions are highly relevant for advancing qubit control strategies in quantum computing.
  • This work expands the toolkit for theoretical investigations in quantum mechanics and related fields.