Related Experiment Video
Updated: Sep 28, 2025
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
8.6K
Geometric energy transfer in two-component systems
Ryan Requist1, Chen Li2, Eberhard K U Gross1
1Fritz Haber Center for Molecular Dynamics, Institute of Chemistry Hebrew University of Jerusalem, Safra Campus, Jerusalem 91904, Israel.
Summary
Researchers partitioned subsystem kinetic energy by factoring wave functions. This method separates energy contributions dependent on marginal and conditional wave functions, offering new insights into quantum mechanics without the Born-Oppenheimer approximation.
Area of Science:
- Quantum mechanics
- Theoretical chemistry
Background:
- The Born-Oppenheimer approximation is a cornerstone of molecular quantum mechanics.
- Investigating methods beyond this approximation is crucial for understanding complex chemical systems.
Purpose of the Study:
- To explore a novel method for factoring wave functions into marginal and conditional components.
- To analyze the partitioning of subsystem kinetic energy based on this factorization.
Main Methods:
- Factoring a wave function into marginal and conditional parts.
- Analyzing the gauge-covariant derivative of the marginal wave function.
- Investigating the quantum metric of the conditional wave function.
Main Results:
- The subsystem kinetic energy is partitioned into two distinct terms.
- The first term depends on the marginal wave function and its gauge-covariant derivative.
- The second term depends on the quantum metric of the conditional wave function.
Conclusions:
- The derived identity for the rate of change of the second kinetic energy term provides a new analytical tool.
- This factorization offers a pathway to explore quantum phenomena beyond the Born-Oppenheimer approximation in chemistry.
Related Concept Videos
01:13Kinetic Energy for a Rigid Body
304
Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.
304
01:16Energy Transfer in Chemical Reactions
9.8K
Chemical reactions require sufficient energy to cause the matter to collide with enough precision and force that old chemical bonds can be broken and new ones formed. In general, kinetic energy is the form of energy powering any type of matter in motion. Imagine a person building a brick wall. The energy it takes to lift and place one brick on top of another is the kinetic energy—the energy matter possesses because of its motion. Once the wall is in place, it stores potential energy.
9.8K
01:14Energy Diagrams - I
5.1K
The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...
5.1K
01:22Mechanical Systems
320
Mechanical systems are analogous to to electrical networks where springs and masses play similar roles to inductors and capacitors, respectively. A viscous damper in mechanical systems functions similarly to a resistor in electrical networks, dissipating energy. The forces acting on a mass in such systems include an applied force in the direction of motion, counteracted by forces from the spring, a viscous damper, and the mass's acceleration. This interplay of forces is mathematically...
320
01:12Conservation of Energy: Application
7.1K
When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy conservation, we study more than one body at the same time. Second, identify all forces acting on the object and determine whether each force doing work is conservative. If a non-conservative force (e.g., friction) is doing work, then mechanical energy is not conserved. The system must then be analyzed with non-conservative work. Third, for...
7.1K
01:22Energy Carried By Electromagnetic Waves
3.2K
Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun's warmth. At other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells. Electromagnetic waves bring energy into a system through their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. However, there is energy in an electromagnetic wave,...
3.2K