Question about this Radial function Rl(r)

Thread starter physicss
Start date Jun 8, 2023
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Radial

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Jun 8, 2023

physicss

Homework Statement: Helllo, I have to show that ∆(R1(r)Y11(ϑ,ϕ)) = 0. I already solved the Y11 part but what is R1(r) or generally written Rl(r) written out? I only know the radial function Rn,l(r). Thanks in advance

Relevant Equations: ∆(R1(r)Y11(ϑ,ϕ)) = 0

Y11
I can´t find Rl(r) written out on the internet.

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Jun 8, 2023

berkeman

Mentor

Are you asking how to take a derivative in spherical coordinates?

https://en.wikipedia.org/wiki/Spherical_coordinate_system

If not, what is the exact problem statement from your assignment?

1. What is a Radial Function?

A radial function is a mathematical function that depends on the distance from a fixed point, known as the origin. It is often used in physics and engineering to describe the behavior of a system in terms of its distance from the origin.

2. What is the significance of the letter "l" in Rl(r)?

The letter "l" in Rl(r) represents the angular momentum quantum number, which is a quantum number used to describe the energy levels of an atom or molecule. It determines the shape of the orbital of an electron in an atom or molecule.

3. How is a Radial Function different from an Angular Function?

A radial function depends on the distance from the origin, while an angular function depends on the angle of rotation around the origin. In other words, a radial function describes the behavior of a system in terms of its distance, while an angular function describes its behavior in terms of its orientation.

4. What is the relationship between a Radial Function and a Wave Function?

A wave function is a mathematical function that describes the behavior of a quantum system, such as an electron in an atom. A radial function is one component of a wave function, specifically the part that describes the behavior of the system in terms of its distance from the origin.

5. How are Radial Functions used in Quantum Mechanics?

In quantum mechanics, radial functions are used to describe the behavior of a system in terms of its distance from the origin. They are an important component of the wave function, which is used to calculate the probability of finding a particle at a certain location in space. Radial functions are also used to calculate the energy levels of an atom or molecule.