Particle in a well potential/energy continuity

In summary, a particle in a well potential/energy continuity refers to a particle trapped in a confined region of space with boundaries created by a potential energy barrier. This particle behaves like a wave and its energy levels are quantized. The potential energy barrier plays a crucial role in determining the particle's behavior, and encountering a barrier may cause the particle's energy to change. Real-world applications of this concept include studying semiconductor devices, modeling atomic and molecular systems, and designing quantum computing algorithms.
  • #1
Sheldon Cooper
21
0
Hello again,
Am facing a difficulty, the question is that ,
Is energy and momentum conserved for a particle in an infinite square well, at the boundary i.e, at x=a, where the potential suffers an infinite discontinuity??
V=0 for -a<=x<=a
V=infinite else-where
Thanks in advance :smile:
 
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  • #2
Yes it is. The particle can't penetrate an infinitely high potential barrier, so it completely reflects there. (provided this isn't classical mechanics with an inelastic collision!)
 
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Likes Sheldon Cooper
  • #3
Did I forget the :welcome: ?

welcome to PF ! :smile:
 

Related to Particle in a well potential/energy continuity

1. What is a particle in a well potential/energy continuity?

A particle in a well potential/energy continuity refers to a concept in quantum mechanics where a particle is trapped in a potential well, meaning it is confined to a certain region of space with boundaries created by a potential energy barrier. Energy continuity refers to the fact that the particle's energy must remain constant within the well.

2. How does a particle behave in a well potential?

In a well potential, a particle behaves in a wave-like manner, with its position and momentum described by a wave function. The particle's energy levels are quantized, meaning they can only take on certain discrete values. The particle's behavior is determined by the Schrödinger equation, which describes the time evolution of the wave function.

3. What is the significance of the potential energy barrier in a particle in a well?

The potential energy barrier in a particle in a well plays a crucial role in determining the behavior of the particle. It acts as a boundary, confining the particle to a certain region of space. The height and width of the barrier also affect the energy levels and the probability of the particle tunneling through the barrier.

4. How does the energy of the particle change when it encounters a potential energy barrier?

When a particle encounters a potential energy barrier, its energy may change depending on the height and width of the barrier. If the particle's energy is lower than the barrier, it will be reflected back, while if the energy is higher, the particle may tunnel through the barrier. In both cases, the particle's energy remains constant within the well.

5. What real-world applications does the concept of a particle in a well potential/energy continuity have?

The concept of a particle in a well potential/energy continuity has various applications, such as in the study of semiconductor devices, where electrons are confined in potential wells. It is also used in the modeling of atomic and molecular systems, as well as in the design of quantum computing algorithms.

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