Second order correction to the wavefunction

In summary, the conversation discusses the derivation of the 2nd order correction to the wave function in perturbation theory. The speaker is looking for a reference text on the topic and mentions a calculation that uses a different normalization.
  • #1
robbo96
1
0
Hi all,

I've been doing a lot of thinking and I was wondering precisely how the 2nd order correction to the wave function from perturbation theory is derived:


6bb97b3cfe3c9497f1a34e3deca4d307.png


6e3eecb34a9ed639b8d6b94e5cb9d731.png


I mean, I can see where bits and pieces come from and I've tried to work through it as an exercise. Does anyone have a reference text on this that they can point me in the direction of? I've exhausted myself looking.

thanks!


Robert
 
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  • #2
http://www.physics.thetangentbundle.net/wiki/Quantum_mechanics/time-independent_perturbation_theory

Note that this calculation uses the normalization [itex]\langle n|n^{(0)}\rangle=1[/itex], and the result is missing your last term. This comes from changing the normalization to [itex]\langle n|n\rangle=1[/itex].
 
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FAQ: Second order correction to the wavefunction

What is a second order correction to the wavefunction?

A second order correction to the wavefunction is a term that is added to the original wavefunction to improve its accuracy in describing the behavior of a quantum system. It takes into account the interaction of the particles in the system and can account for deviations from the ideal behavior predicted by the original wavefunction.

When is a second order correction necessary?

A second order correction is necessary when the particles in a quantum system are interacting with each other, as this can cause deviations from the ideal behavior predicted by the original wavefunction. In these cases, the second order correction can improve the accuracy of the wavefunction and provide a more complete description of the system.

How is a second order correction calculated?

A second order correction is calculated by using perturbation theory, which involves breaking down the original wavefunction into a series of terms, with the second order term being the most important correction. This calculation involves solving for the second order energy correction and then using this to determine the second order correction to the wavefunction.

What are the limitations of a second order correction?

One limitation of a second order correction is that it can only account for small deviations from the ideal behavior predicted by the original wavefunction. If the interactions between particles are too strong or the deviations are too large, a higher order correction may be necessary. Additionally, the accuracy of the correction depends on the accuracy of the original wavefunction.

How does a second order correction impact the overall wavefunction?

A second order correction can significantly impact the overall wavefunction by improving its accuracy and providing a more complete description of the quantum system. It can also change the energy levels and probabilities associated with the system, and therefore affect the predictions and observations made about the system. Without a second order correction, the wavefunction may not accurately describe the behavior of the particles in the system.

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