Infinite well with two regions

In summary, the conversation is about a particle with energy greater than the potential energy level inside an infinite well with two distinct regions. The question is whether the wavenumber k of the particle is larger in Region A, where the potential energy is zero, or in Region B, where the potential energy level is U0. The original question was about the wavenumber, but it was changed to the wavelength, which is inversely related to the wavenumber. The correct answer is Region B, where the wavenumber is larger.
  • #1
soothsayer
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Imagine an infinite well with two distinct regions in it. In Region A, potential energy is zero, however, Region B has a potential energy level of U0. A particle with energy E>U0, is inside the well. In which region is the wavenumber k of the particle larger? A or B?

This was a problem my professor brought up in class, and I was pretty sure the answer was region A, since the wavenumber is proportional to the momentum of the particle, and the momentum is greatest in region A, where there is no potential energy and, therefore, kinetic energy is greater, but my prof. said the answer was B. Perhaps he made a mistake, or maybe I made a mistake (or wrote my notes down wrong) but I don't see how that could be the case, could anyone shed some light on this problem?
 
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  • #2
You are correct, since k is proportional to sqrt(E-V), so clearly region A has greater k
 
  • #3
Ohh, ok, just looked over my notes, and the question was not which region k was bigger in, it was which region the wavelength was larger in, which would be B, since wavenumber and wavelength is inversely related. The reason I got confused was because the original question was which region was k larger, but then he changed it. Thanks anyway!
 

1. What is an "infinite well with two regions" in physics?

An infinite well with two regions, also known as a double well potential, is a type of potential energy function used in quantum mechanics to model the behavior of particles in a specific region. It consists of two separate regions with different potential energy values, separated by a barrier. This potential is often used to study the behavior of particles in a confined space, such as a molecule or an atom.

2. How does an infinite well with two regions work?

The potential energy function of an infinite well with two regions is described by a piecewise function, where the potential energy is constant in each region and increases abruptly at the barrier. The regions act as "wells" where the particle can be confined, while the barrier prevents the particle from escaping. The behavior of the particle in this system can be studied using the Schrödinger equation and the wave function of the particle.

3. What are the applications of an infinite well with two regions?

An infinite well with two regions has various applications in physics, especially in quantum mechanics. It can be used to study the behavior of particles in confined spaces, such as in semiconductors, where electrons are confined to a small region. It is also used to model the behavior of atoms and molecules. Additionally, the double well potential has applications in optics, where it is used to study the behavior of light waves passing through a medium with varying refractive indices.

4. What are the key features of an infinite well with two regions?

The key features of an infinite well with two regions include the presence of two separate regions with different potential energy values, a barrier separating the two regions, and the confinement of particles within the two regions due to the potential energy profile. The potential energy function is also continuous and differentiable at the boundary between the two regions, allowing for the use of mathematical techniques to analyze the system.

5. How does the behavior of a particle in an infinite well with two regions differ from that in a single well?

The behavior of a particle in an infinite well with two regions differs from that in a single well in several ways. In a single well, the particle is confined to a single region, while in a double well, it has the potential to exist in two separate regions. Additionally, the presence of a barrier in a double well potential can lead to interesting phenomena, such as tunneling, where the particle can pass through the barrier even if it does not have enough energy to overcome it. This is not possible in a single well potential.

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