Dirac delta spherical potential

In summary, a Dirac delta spherical potential is a mathematical concept used to describe the potential field around a point charge or point mass in three-dimensional space. It is a more general form of a point charge or point mass potential and has various applications in physics and engineering. It is defined as a function that is zero everywhere except at the origin, where it has an infinite value, and it can be represented graphically by plotting potential values at different distances from the origin.
  • #1
neworder1
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Homework Statement



Three-dimensional particle is placed in a Dirac delta potential:

[tex]V = -aV_{0}\delta(r-a)[/tex]

Find energy states and eigenfunctions for the angular quantum number [tex]l = 0[/tex].[/


Homework Equations





The Attempt at a Solution



It's not clear to me what boundary conditions will do in this case - is this analogous to 1D case?
 
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  • #2
Same as in all central potential problems.
 

1. What is a Dirac delta spherical potential?

A Dirac delta spherical potential is a mathematical concept used to describe the potential field around a point charge or a point mass in three-dimensional space. It is a radial potential that follows the inverse-square law, meaning that the strength of the potential decreases with distance from the point charge or point mass.

2. How is a Dirac delta spherical potential different from a point charge or point mass potential?

A Dirac delta spherical potential is a more general form of a point charge or point mass potential. While a point charge or point mass potential is only valid for a discrete point, a Dirac delta spherical potential can be used to describe the potential field around a distribution of point charges or point masses. It is also continuous, meaning that it can be defined at any point in space.

3. What are the applications of a Dirac delta spherical potential?

A Dirac delta spherical potential has various applications in physics and engineering. It is commonly used in electrostatics and gravitational potential calculations, as well as in the study of atomic and molecular interactions. It is also used in the calculation of potentials in spherical coordinate systems.

4. How is a Dirac delta spherical potential mathematically defined?

A Dirac delta spherical potential is mathematically defined as a function that is zero everywhere except at the origin, where it has an infinite value. This point of infinite value is known as a Dirac delta function, and it is represented by the symbol δ. In mathematical notation, a Dirac delta spherical potential can be written as V(r) = k δ(r), where k is a constant and r is the distance from the origin.

5. Can a Dirac delta spherical potential be visualized?

Since a Dirac delta spherical potential is a mathematical concept, it cannot be directly visualized. However, it can be represented graphically by plotting the potential values at different distances from the origin. This can help in understanding how the strength of the potential changes with distance and how it affects the behavior of charged particles or masses in its field.

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