Energy levels from the Schrodinger eqn

In summary, the question is asking for help in calculating energy levels from the Schrodinger equation, specifically for a particle in a uniform magnetic field with no potential. The person asking the question has successfully dealt with the potential but is struggling to understand how their teacher has determined the potential energy to be V=kx^2. They are looking for clarification on the steps taken to reach this conclusion.
  • #1
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Homework Statement


I'm just wondering how you get the energy levels from the Schrodinger equation. I've got the equation in the form H(psi) = E(psi) with all the H expanded out, I just don't know how to calculate the energy levels from it. Its probably something I did once know how to do, but for the time being it has slipped my mind. Any help would be appreciated.

In the example I'm looking at (and following to an extent) its a particle in a uniform magnetic field that's perpendicular to the motion of the particle, but with no potential amd he suddenly says that its clearly a harmonic oscillator and that the energy levels are obvious the normal value for such.

In our question we have a potential that I have dealt with (succesfully I think) and I've followed up until this point that I mentioned. But I can't see how he made the step that he did. I'm pretty sure that this is just a standard method, but I can provide the specific examples if required for this (my tex isn't great, so I'm trying to avoid it where possible!).

Thanks for any help


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  • #2
To find the energy levels you need to know the potential - your teacher is saying that the potential energy goes like V=kx^2 -> but i don't understand how he's coming to that conclusion either.
 

What is the Schrodinger equation?

The Schrodinger equation is a mathematical equation that describes the behavior of quantum systems, such as atoms and molecules. It was developed by Austrian physicist Erwin Schrodinger in 1926.

What are energy levels from the Schrodinger equation?

Energy levels from the Schrodinger equation refer to the discrete and quantized energy states that a particle can occupy in a quantum system. These energy levels are determined by solving the Schrodinger equation.

How are energy levels from the Schrodinger equation calculated?

Energy levels from the Schrodinger equation are calculated by solving the equation for a particular quantum system. This involves determining the wavefunction of the system, which describes the probability of finding the particle at a given position, and using it to calculate the energy levels.

What is the significance of energy levels from the Schrodinger equation?

The energy levels from the Schrodinger equation provide important information about the behavior and properties of quantum systems. They determine the allowed energy states of particles in a system, and how those particles interact with each other and their surroundings.

Can the Schrodinger equation be used to calculate energy levels for all quantum systems?

Yes, the Schrodinger equation can be used to calculate energy levels for all quantum systems, as long as the system is described by a wave function and the potential energy is known. However, for more complex systems, the equation may need to be solved numerically rather than analytically.

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