Infinite Square Well with Multiple Particles

Thread starter sarahjohn
Start date Jul 7, 2021
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Infinite Infinite square well Multiple Particles Square Square well

In summary, an infinite square well with multiple particles is a theoretical model used to study the behavior of particles in a confined space. The well potential creates a barrier that restricts the particles, and the boundary conditions are crucial in determining their energy levels and wave functions. This system can have particles with different masses, which affects the depth of the well potential and subsequently, the energy levels and wave functions. The number of particles also affects the system by causing repulsion between them, resulting in a splitting of energy levels and modification of their wave functions.

Jul 7, 2021

sarahjohn

Homework Statement: An infinitely deep square well has width L = 2.5 nm. The potential energy is V = 0 eV inside the well (i.e., for 0 ≤ x ≤ L). Seven electrons are trapped in the well.

1)What is the ground state (lowest) energy of this seven electron system?
2)What is the energy of the first excited state of the system?
NOTE: The first excited state is the one that has the lowest energy that is larger than the ground state energy.
3)What is the energy of the second excited state of the system?

Relevant Equations: En = (h^2 * n^2) / (8 * m * L^2)

Using the equation En = (h²*n² ) / (8*m*L²), I got that E1 = 0.06017eV but the answer is not correct.

Last edited: Jul 7, 2021

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Jul 7, 2021

TSny

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Have you taken into account that you have seven electrons?

Jul 9, 2021

sarahjohn

TSny said:

Have you taken into account that you have seven electrons?

I realized that was my mistake and figured it out. Thank you!

1. What is an "Infinite Square Well with Multiple Particles"?

An Infinite Square Well with Multiple Particles is a theoretical model used in quantum mechanics to describe the behavior of multiple particles confined within a potential well. This model assumes that the particles are non-interacting and are confined within an infinitely high potential barrier, creating a well with finite boundaries.

2. How does the potential well affect the particles in this model?

The potential well in this model acts as a barrier that confines the particles within a finite region. The particles are only allowed to exist within this region and cannot escape beyond the boundaries of the well. This creates a discrete energy spectrum for the particles, with only certain energy levels being allowed within the well.

3. What is the significance of the term "infinite" in this model?

The term "infinite" in this model refers to the potential barrier, which is assumed to be infinitely high. This means that the particles are completely confined within the well and cannot escape. It also allows for the simplification of the mathematical equations used to describe the behavior of the particles.

4. How does this model differ from the single particle Infinite Square Well model?

In the single particle Infinite Square Well model, there is only one particle confined within the potential well. In the multiple particle model, there are multiple particles confined within the same well. This means that the energy levels and wave functions of the particles in the multiple particle model are affected by the presence of other particles, whereas in the single particle model they are not.

5. What are some practical applications of the Infinite Square Well with Multiple Particles model?

The Infinite Square Well with Multiple Particles model is mainly used as a theoretical tool to understand the behavior of particles in quantum systems. It can be applied to various systems, such as atoms in a crystal lattice or electrons in a metal. It also has applications in understanding the behavior of particles in quantum computing and quantum information processing.