Calculating Spherical Harmonics Cuadratic Dispersion

In summary, the conversation discusses the process of calculating quadratic dispersion for quantum systems by expanding x^2 in terms of spherical harmonics using Clebsch-Gordan coefficients or threeJ. The speaker mentions starting from the expansion of x and then calculating x^2 by studying the couplings of the state vectors. They also mention needing help with the correct sum of spherical harmonics.
  • #1
altered-gravity
62
0
Greetings,

I´m calculating cuadratic dispersion of some quantum systems. I need to expand x^2 in terms of spherical harmonics (using Clebsch-Gordan coefficients, or threeJ as well) in order to be able to use Gaunt espression in the integral solving.

I start from the expansion of x as linnear combination of Spherical Harmonics (with Clebsch-Gordan coef.). Then, in order to get x^2, I calculate x*x (studying the couplings of the state vectors term by term) and I get what I need: a sum of Spherical Harmonics (each multiplied by a C-G coef.) but it´s not the correct one!

Could anyone help me? Thanks
 
Physics news on Phys.org
  • #2
wow K-12 got really hard really fast!
sorry, maybe a different forum should be addressed
 
  • #3
oops! Excuse me.
 

1. What are spherical harmonics?

Spherical harmonics are mathematical functions used to describe the angular dependence of quantum states in three-dimensional space. They are commonly used in the study of atomic and molecular systems, as well as in solving problems in electromagnetism and fluid dynamics.

2. How are spherical harmonics calculated?

The calculation of spherical harmonics involves integrating a complex-valued function over the surface of a sphere. This is typically done using numerical methods such as the Gauss-Legendre quadrature. Alternatively, analytical expressions for the spherical harmonics can be derived using the Laplace equation.

3. What is cuadratic dispersion in relation to spherical harmonics?

Cuadratic dispersion refers to the relationship between the energy and momentum of a particle in a material. In the context of spherical harmonics, it describes the energy levels of a quantum state as a function of its angular momentum and spatial orientation. This can be calculated using the spherical harmonics and the Schrödinger equation.

4. What is the significance of calculating spherical harmonics cuadratic dispersion?

Calculating spherical harmonics cuadratic dispersion allows us to understand the behavior of particles in a material, particularly in relation to their energy levels and angular momentum. This is important in fields such as solid-state physics and materials science, where the properties of materials are closely tied to the behavior of their constituent particles.

5. Are there any practical applications of calculating spherical harmonics cuadratic dispersion?

Yes, there are many practical applications of calculating spherical harmonics cuadratic dispersion. These include understanding the electronic properties of materials, predicting the behavior of particles in magnetic fields, and developing new materials with specific properties for various applications. Additionally, spherical harmonics cuadratic dispersion is often used in the development of quantum computing algorithms and in the study of quantum information theory.

Similar threads

I Transforming Cartesian Coordinates in terms of Spherical Harmonics
    • Differential Equations
Replies
1
Views
2K
Analysis Resource(s) for introduction to spherical harmonics with exercises?
    • Science and Math Textbooks
Replies
14
Views
1K
I Spherical Harmonics Expansion convergence
    • Linear and Abstract Algebra
Replies
6
Views
2K
How to calculate a sink using spherical coordinates
    • Calculus and Beyond Homework Help
Replies
7
Views
699
I Second Matrices from Spherical Harmonics with Eigenvalue l+1
    • Quantum Physics
Replies
8
Views
1K
Expanding potential in Legendre polynomials (or spherical harmonics)
    • Advanced Physics Homework Help
Replies
1
Views
1K
B Method of images and spherical coordinates
    • Electromagnetism
Replies
4
Views
804
I Alternating Harmonic Numbers are cool, spread the word!
    • General Math
Replies
4
Views
408
A Pair of interacting systems, driven coupled harmonic oscillators
    • Mechanics
Replies
7
Views
639
Coefficient Matching for different series
    • Calculus and Beyond Homework Help
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top