Quick question about a simple perturbation theory question

So, in summary, a particle of charge q and mass m in a harmonic oscillator potential V0=0.5m(wx)^2 experiences a perturbation of V=V0 + dV, where dV=0.5sm(wx)^2 and s is small. To compute the first order shift in the ground state energy, perturbation theory is used, with the equation E0' - E0 = <0|h|0>. The Hamiltonian for a SHO typically only has 0.5m(wx)^2 as the potential term, but in this case, q is used to calculate the potential energy.
  • #1
joker_900
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Homework Statement


A particle of charge q and mass m is in a harmonic oscillator potential V0=0.5m(wx)^2. A perturbation is introduced which changes the potential to V=V0 + dV with dV=0.5sm(wx)^2 where s is small.

Use perturbation theory to compute the first order shift in the ground state energy.


Homework Equations


E0' - E0 = <0|h|0>


The Attempt at a Solution


Well I've done it ish but am kind of confused about where the q is supposed to be used. Should I multiply V0 by q to get the potential energy, and use that in H?

I'm used to the hamiltonian for a SHO just having 0.5m(wx)^2 as the potential term.

Thanks
 
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  • #2
Energy is charge times electric field, so q times V is energy.
 

FAQ: Quick question about a simple perturbation theory question

What is perturbation theory?

Perturbation theory is a mathematical method used to approximate the solutions of a problem by introducing a small parameter into the system and solving for the solution in a series of iterations.

Why is perturbation theory important?

Perturbation theory is important because it allows us to approximate solutions for complex systems that are difficult to solve exactly. It is used in many fields, including physics, chemistry, and engineering.

How does perturbation theory work?

Perturbation theory works by introducing a small parameter, usually denoted as ε, into the equations that describe a system. The solution is then calculated in a series of iterations, with each iteration taking into account the effects of the parameter on the system.

What are the limitations of perturbation theory?

One limitation of perturbation theory is that it only works for small perturbations. If the perturbation is too large, the series will not converge and the solution will not be accurate. Additionally, perturbation theory may not work for highly nonlinear systems.

How is perturbation theory used in practical applications?

Perturbation theory is used in many practical applications, such as calculating the energy levels of atoms and molecules in quantum mechanics, predicting the orbits of planets in celestial mechanics, and studying the stability of systems in engineering. It is also used in computer simulations to model complex systems.

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