Solve Particle-on-a-Ring Problem: Normalize & Write as Linear Combination

In summary, the conversation discusses a problem involving a particle on a ring and the wavefunction g(phi) = cos(phi) + 2sin(2phi). The first step is to normalize g(phi) and then write it as a linear combination of eigenfunctions of Lz. The possible results for a measurement of Lz in this state are also mentioned, along with their corresponding probabilities. The relevant equation for Lz and a request for attempted workings are also mentioned.
  • #1
evildarklord1985
11
0
I have troubles to do this one problem dealing with particle-on-a-ring,

Suppose we have a wavefunction as,
g(phi) = cos(phi) + 2 sin(2phi)

First, normalize the function g(phi). By inspection, or otherwise, write g(phi) as a linear combination of eigenfunction of Lz. State what possible results for a measurement of Lz in this state would be, and what would be the corresponding probablities to obtain each one values.

Thanks for any helps!
 
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  • #2
Per the rules of the forum, you have to show some attempted workings...

Relevant equations:

[tex]L_z = -i \hbar \partial_\phi[/tex]

Can you find the eigenfunctions?
 

FAQ: Solve Particle-on-a-Ring Problem: Normalize & Write as Linear Combination

What is the particle-on-a-ring problem?

The particle-on-a-ring problem is a classic physics problem that involves a particle moving in a circular path on a ring. This problem is often used to demonstrate concepts such as angular momentum, centripetal force, and energy conservation.

What does it mean to normalize the particle-on-a-ring problem?

Normalizing the particle-on-a-ring problem involves finding the maximum possible value for the wavefunction of the particle, which is necessary for solving the problem using quantum mechanics. This allows us to scale the wavefunction and make it easier to work with.

How do you write the particle-on-a-ring problem as a linear combination?

To write the particle-on-a-ring problem as a linear combination, we use the normalization constant found in the previous step to scale the wavefunction. This allows us to express the wavefunction as a sum of different states with different energies, which can then be used to solve the problem.

What are some applications of the particle-on-a-ring problem?

The particle-on-a-ring problem has applications in various fields of physics, including quantum mechanics, statistical mechanics, and solid state physics. It is also commonly used as a model for understanding the behavior of electrons in atoms and molecules.

Is the particle-on-a-ring problem a realistic scenario?

No, the particle-on-a-ring problem is a simplified scenario that is used to demonstrate specific concepts in physics. In reality, particles do not move in perfectly circular paths and are subject to various other forces. However, this problem allows us to understand and analyze certain physical phenomena in a controlled and simplified manner.

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