Electron in infinite well equation

In summary, the "Electron in infinite well equation" is a mathematical expression used to describe the energy levels and wave function of an electron in a confined space. It is derived from the Schrödinger equation and makes assumptions about the walls and potential of the well. The equation helps us understand the quantization of energy levels and serves as a model for more complex systems. While it is not accurate for real-world systems, it can provide valuable insights for further calculations and experiments.
  • #1
ZedCar
354
1

Homework Statement



An electron is confined in an infinitely deep well of width 0.1nm, about the size of an atom. Estimate the energy of the ground state in eV.

Homework Equations



Is this the equation I should be using?

E=(n^2 hbar^2 ∏^2)/(2m L^2)



The Attempt at a Solution

 
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  • #2
ZedCar said:
Is this the equation I should be using?
Yes, assuming you're using 1-dimension. (The way the problem statement was worded, it sounds to me like 1-dimentional quantum mechanics is a reasonable assumption.)
 

1. What is the "Electron in infinite well equation"?

The "Electron in infinite well equation" is a mathematical expression used to describe the energy levels and wave function of an electron confined to an infinite potential well. It is a simplified model used in quantum mechanics to understand the behavior of particles in a confined space.

2. How is the "Electron in infinite well equation" derived?

The equation is derived from the Schrödinger equation, which is the fundamental equation of quantum mechanics. By applying boundary conditions to the Schrödinger equation, the solution for the energy levels and wave function of an electron in an infinite potential well can be obtained.

3. What are the assumptions made in the "Electron in infinite well equation"?

The equation assumes that the walls of the potential well are infinitely high, meaning that the electron cannot escape. It also assumes that the potential inside the well is constant and the electron has no interactions with other particles.

4. What is the significance of the "Electron in infinite well equation"?

The equation helps us understand the quantization of energy levels in a confined space. It also serves as a simple model for understanding the behavior of electrons in more complex systems, such as atoms and molecules.

5. Can the "Electron in infinite well equation" be applied to real-world systems?

The equation is a simplified model and does not accurately represent real-world systems. However, it can still provide valuable insights and serve as a starting point for more complex calculations and experiments.

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