量子状态类似于介面镜圆形亿博游戏中的经典周期轨迹
Jesús G Riestra1, Julio C Gutiérrez-Vega1
1Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey 64849, Mexico.
Physical review. E
|April 18, 2024
概括
研究人员将量子波函数定位在圆形的周期轨道上. 这种量子-经典对应性是通过叠加特定的量子状态来实现的,揭示了对运动模式的洞察力.
科学领域:
- 量子力学就是量子力学.
- 经典机械学 经典机械学
- 中视镜系统 (mesoscopic systems) 是一种中视镜系统.
- 数学物理学的数学物理.
背景情况:
- 了解量子力学和经典力学之间的对应关系是一个根本的挑战.
- 介面镜系统提供了一个独特的制度,以古典类比来探索量子现象.
- 圆球提供了一个明确的系统,用于研究古典和量子动力学.
研究的目的:
- 为了实现量子波函数的局部化,将它们定位在一个半球体圆形亿球体内的经典周期轨道上.
- 在量子状态的背景下分析旋转和 librational 运动模式.
- 通过积分方程,建立量子态和经典轨迹之间的联系.
主要方法:
- 几乎退化的固态的叠加,表达为马修函数的积分.
- 使用概率电流密度,相位图和分布来分析量子状态.
- 通过积分方程从量子状态提取代表经典轨迹的简化直线方程.
主要成果:
- 成功地将局部量子波函数定位到圆亿球中的经典周期轨道上.
- 为这些量子状态确定了不同的旋转和 librational 运动模式.
- 积方程中的相位因子将量子状态与经典的初始位置和速度相关联.
结论:
- 这项研究展示了一种在圆亿球中弥合量子定位和经典周期轨道的方法.
- 量子状态可以代表移动和静止的轨迹,反映经典运动.
- 这些发现为人们更深入地理解了介光系统中的量子-经典对应.
相关概念视频
02:32The de Broglie Wavelength
25.9K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
25.9K
02:45The Quantum-Mechanical Model of an Atom
42.3K
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.
42.3K
02:43Quantum Numbers
34.7K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
34.7K
01:28Conservation of Linear Momentum for a System of Particles
223
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
223
01:18First Law: Particles in Two-dimensional Equilibrium
5.1K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
Newton's first law tells us about...
5.1K
01:10First Law: Particles in One-dimensional Equilibrium
6.9K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
6.9K