Matriz Lz, m=2, but in x,y,z basis

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In summary, the conversation discusses the differences between the matrix ##J_z## in spherical harmonics basis and cartesian basis. While in spherical harmonics basis the matrix is diag(2,1,0,-1,-2), in cartesian basis it is represented by i h(0,-1,0)(1,0,0),(0,0,0). The conversation also raises the question of how the matrix ##J=2## can be mapped to three-dimensional cartesian space.
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alejandrito29
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I don't see how you can map ##J=2## to three-dimensional cartesian space.
 

1. What is Matriz Lz, m=2?

Matriz Lz, m=2 is a mathematical representation of the angular momentum operator in quantum mechanics. In simpler terms, it is a way to describe the rotation of a particle in three-dimensional space.

2. How is Matriz Lz, m=2 related to x,y,z basis?

Matriz Lz, m=2 is commonly expressed in terms of the x,y,z basis because this is the most convenient coordinate system for describing three-dimensional rotations. The matrix elements of Matriz Lz, m=2 correspond to the rotation of a particle about the x,y,z axes.

3. What does the value of m=2 represent in Matriz Lz, m=2?

The value of m=2 in Matriz Lz, m=2 represents the specific angular momentum state of a particle. In other words, it indicates the orientation and rotational energy of the particle. Different values of m correspond to different energy levels and orientations.

4. How is Matriz Lz, m=2 used in quantum mechanics?

Matriz Lz, m=2 is an important tool in quantum mechanics for understanding the behavior of particles with angular momentum. It is used to calculate the expected values of angular momentum for different states of a particle, and to study the effects of external forces on the particle's rotation.

5. Is Matriz Lz, m=2 the same for all particles?

No, the specific form of Matriz Lz, m=2 can vary depending on the type of particle and its properties, such as its spin and mass. However, the general concept of representing angular momentum in terms of a matrix is applicable to all particles in quantum mechanics.

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