Solving Angular Momentum Homework: Lx = h

In summary, the conversation discusses the most likely outcome of the next measurement of Lz, given that Lx has been measured to be h. The speaker describes two methods they have tried, one involving solving for the eigenvalues/eigenstates of Lx in a |lm> basis and the other involving taking the projection between Lz and Lx. The speaker expresses uncertainty and hopes for a better method. However, they later figure out that solving for the eigenvalues/eigenstates of Lx is sufficient. They wonder how this method compares to the other one they tried.
  • #1
myradiogalaxy
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Homework Statement


Lx is measured to be h, what is the most likely outcome of the next measurement of Lz


Homework Equations





The Attempt at a Solution


So far I built the matrix Lx with |lm> basis where |lm> is a eigenfunction of Lz, for l =1.

Not being not sure where to go from there I went for a more direct method of taking the projection < lz, mz | lx=1, mx=1> and solving it, and the one with the largest magnitude would win. But the only way I could figure that would be to expand < lz, mz | lx=1, mx=1> into < lz, mz | n >< n l lx=1, mx=1>, where n is the directional eigenket, which I believe gives two spherical harmonics where later has to be rotated from x to z.

To sum up I feel pretty insecure about all this and hope there's a better way.
 
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  • #2
Ok I figured it out. Solving for the eigenvalues/eigenstates for Lx in a |lm> basis was all I had to do. I wonder how it would compare to that other method.
 

1. What does "Lx = h" represent in angular momentum?

"Lx = h" is a representation of the quantized angular momentum in the x-direction. It is a mathematical expression that relates the angular momentum (L) to the reduced Planck's constant (h) in a quantum mechanical system.

2. How is angular momentum solved using "Lx = h"?

In order to solve for angular momentum using "Lx = h", you need to know the value of reduced Planck's constant (h) and the angular momentum operator (Lx). The angular momentum operator is a mathematical expression that represents the observable quantity of angular momentum in a quantum mechanical system. Once you have these values, you can simply plug them into the equation "Lx = h" to solve for the angular momentum.

3. What are some real-world applications of "Lx = h" in solving angular momentum?

"Lx = h" is a fundamental equation in quantum mechanics and is used to describe the behavior of particles at the atomic and subatomic levels. It has various applications in fields such as nuclear physics, solid-state physics, and atomic and molecular physics. Some specific applications include understanding the behavior of electrons in atoms, predicting the rotational energy levels of molecules, and calculating the spin of particles.

4. What is the significance of "Lx = h" in the study of quantum mechanics?

The equation "Lx = h" is significant in the study of quantum mechanics because it relates the quantized angular momentum to the reduced Planck's constant, a fundamental constant in quantum mechanics. It is an essential tool in understanding the behavior of particles at the atomic and subatomic levels, and has been used to make many important predictions and calculations in the field of quantum mechanics.

5. Are there any other equations or principles related to "Lx = h" in the study of angular momentum?

Yes, there are other equations and principles related to "Lx = h" in the study of angular momentum. The equation "Lx = h" is part of a larger set of equations known as the angular momentum operators, which also include Ly and Lz. Additionally, there are other principles, such as the conservation of angular momentum, that are essential in understanding and solving problems related to angular momentum.

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