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

Fischer Projections02:18

Fischer Projections

16.4K
Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines. While...
16.4K
Newman Projections02:06

Newman Projections

20.7K
Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as...
20.7K
Coordinates and Map Projections01:29

Coordinates and Map Projections

603
Coordinates and map projections are essential tools in accurately representing the Earth's surface for various applications, ranging from navigation to spatial analysis. The latitude and longitude coordinate system is a universally recognized framework for defining locations. Latitude specifies the distance of a point north or south of the equator, measured in degrees from 0° at the equator to 90° at the poles. Longitude indicates a location's position east or west of the prime meridian,...
603
Operational Amplifiers01:17

Operational Amplifiers

1.9K
The operational amplifier, often referred to as an op-amp, is a multifaceted building block of a circuit. This electronic component functions like a voltage-controlled voltage source and can also be used to create a voltage- or current-controlled current source. The design of an operational amplifier enables it to execute mathematical operations when external components like resistors and capacitors are linked to its terminals. An op-amp has the capacity to sum signals, amplify a signal,...
1.9K
Vector Operations01:20

Vector Operations

2.2K
Vectors are physical quantities that have both magnitude and direction. The vector operations include addition, subtraction, and scalar multiplication.
A vector multiplied by a scalar value is called scalar multiplication. The result obtained is a new vector with a different magnitude. If the scalar is positive, the direction of the vector remains the same, but if it is negative, the direction of the vector is reversed. For example, the product of the mass and velocity yields the momentum.
2.2K
Operant Conditioning01:21

Operant Conditioning

2.8K
Operant conditioning, a key concept in behavioral psychology, involves using reinforcement and punishment to alter the likelihood of a behavior being repeated. B.F. introduced this type of conditioning. Skinner focused on voluntary behaviors and the consequences that follow them, influencing whether these behaviors will be strengthened or diminished.
Reinforcement in operant conditioning can be positive or negative, both of which serve to increase the likelihood of a behavior. Positive...
2.8K

You might also read

Related Articles

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

Sort by
Same author

Accuracy and Resource Advantages of Quantum Eigenvalue Estimation with Non-Hermitian Transcorrelated Electronic Hamiltonians.

Journal of chemical theory and computation·2026
Same author

Exact factorization of unitary transformations with spin-adapted generators.

The Journal of chemical physics·2026
Same author

Quantum Gambling: Best-Arm Strategies for Generator Selection in Adaptive Variational Algorithms.

Journal of chemical theory and computation·2026
Same author

Quantum Seniority-Based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for the Electronic Structure Problem.

Journal of chemical theory and computation·2026
Same author

On the Feasibility of Exact Unitary Transformations for Many-Body Hamiltonians.

Journal of chemical theory and computation·2026
Same author

Multistate Iterative Qubit Coupled Cluster (MS-iQCC): A Quantum-Inspired, State-Averaged Approach to Ground- And Excited-State Energies.

Journal of chemical theory and computation·2026

Related Experiment Video

Updated: Jan 27, 2026

Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System
09:48

Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System

Published on: June 30, 2018

9.3K

On Construction of Projection Operators.

Artur F Izmaylov1,2

  • 1Department of Physical and Environmental Sciences , University of Toronto Scarborough , Toronto , Ontario M1C 1A4 , Canada.

The Journal of Physical Chemistry. A
|March 28, 2019
PubMed
Summary

This study develops projection operators for quantum symmetry, ensuring physical symmetries in approximate methods. This method aids in solving quantum problems and advancing electronic structure calculations and quantum computing.

More Related Videos

Born Normalization for Fluorescence Optical Projection Tomography for Whole Heart Imaging
16:44

Born Normalization for Fluorescence Optical Projection Tomography for Whole Heart Imaging

Published on: June 2, 2009

10.7K
Design and Construction of an Urban Runoff Research Facility
13:48

Design and Construction of an Urban Runoff Research Facility

Published on: August 8, 2014

13.5K

Related Experiment Videos

Last Updated: Jan 27, 2026

Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System
09:48

Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System

Published on: June 30, 2018

9.3K
Born Normalization for Fluorescence Optical Projection Tomography for Whole Heart Imaging
16:44

Born Normalization for Fluorescence Optical Projection Tomography for Whole Heart Imaging

Published on: June 2, 2009

10.7K
Design and Construction of an Urban Runoff Research Facility
13:48

Design and Construction of an Urban Runoff Research Facility

Published on: August 8, 2014

13.5K

Area of Science:

  • Quantum mechanics
  • Computational physics
  • Group theory

Background:

  • Approximate methods in quantum mechanics require projection operators.
  • Ensuring physical symmetries is crucial for the accuracy of these methods.
  • Existing methods face challenges in constructing projection operators for complex symmetry structures.

Purpose of the Study:

  • To develop a general method for constructing projection operators on eigensubspaces of symmetry operators.
  • To ensure proper physical symmetries are maintained in approximate quantum solutions.
  • To provide a framework applicable to both time-independent and time-dependent quantum problems.

Main Methods:

  • The construction involves two key steps: identifying algebraic structures (groups, Lie algebras) among symmetry operators and constructing projection operators based on these structures.
  • Leveraging information from irreducible representations of identified algebraic structures.
  • The projector form is expressed as a function of symmetry operators and their eigenvalues.

Main Results:

  • A systematic approach to constructing projection operators that respect physical symmetries is presented.
  • The method utilizes the algebraic properties of symmetry operators for efficient construction.
  • The developed projection operators are applicable to various quantum problems.

Conclusions:

  • The proposed method provides a robust way to construct projection operators for quantum mechanical applications.
  • This approach can enhance the development of variational methods for electronic structure in strongly correlated systems.
  • The findings have implications for advancing quantum computing algorithms and simulations.