Finite square well potential question

In summary, the conversation discusses the number of bound energy states in a finite one-dimensional square potential well in which a proton is bound. The energy levels are calculated using a formula, but the number of allowed energy states is uncertain due to the finite depth of the potential well. The speaker is seeking assistance in determining the maximum energy level that is less than 40 MeV.
  • #1
StephenD420
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For a finite one-dimensional square potential well if a proton is bound, how many bound energy states are there?

If m = 1.67*10^(-27) kg a = 2.0fm and the depth of the well is 40MeV.

Now I know the energy levels are
En = (n^2 * h^2) /(8ma^2) = (n^2*pi*2)/4 * (2hbar^2)/(ma^2)

but I am unsure as to how to find the number of the allowed energy states. Any help would be greatly appreciated.

Thanks.
Stephen
 
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  • #2
Determine n belonging to the maximum magnitude of energy less then 40 MeV. But take care: the formula you cited refers to infinite potential wells. Here the potential well is of finite depth.

ehild
 
Last edited:

What is a finite square well potential?

A finite square well potential is a type of potential energy function that is commonly used in quantum mechanics to describe the behavior of a particle in a confined space. It is a square-shaped potential well with finite boundaries, meaning that the particle can only exist within a certain range of positions and energies.

What are the key properties of a finite square well potential?

The key properties of a finite square well potential include a finite depth and width, as well as a discontinuous potential energy function at the boundaries. It is also characterized by the presence of bound states, meaning that the particle can exist within the well with a specific energy level.

How is the behavior of a particle in a finite square well potential determined?

The behavior of a particle in a finite square well potential is determined by solving the Schrödinger equation, which describes the evolution of a quantum system over time. The solution to this equation gives the allowed energy levels and corresponding wave functions for the particle within the potential.

What are some real-life applications of the finite square well potential?

The finite square well potential has various applications in fields such as solid state physics, nuclear physics, and atomic physics. It is used to study the behavior of electrons in a crystalline lattice, the energy levels of nuclei in atoms, and the confinement of particles in potential wells in quantum computing.

What are the limitations of the finite square well potential model?

One of the main limitations of the finite square well potential model is that it is a simplified representation of real-life systems. It does not take into account factors such as the shape and size of the potential well, the interactions between particles, and the effects of temperature and external forces. As a result, it may not accurately predict the behavior of particles in complex systems.

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