Second order correction to the wavefunction

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SUMMARY

The discussion focuses on the derivation of the second order correction to the wavefunction in quantum mechanics, specifically within the framework of time-independent perturbation theory. Robert seeks references to better understand this derivation, indicating a need for clarity on the normalization conditions used in the calculations. A key point raised is the difference in normalization between \(\langle n|n^{(0)}\rangle=1\) and \(\langle n|n\rangle=1\), which affects the final result of the perturbative expansion.

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  • Understanding of quantum mechanics principles
  • Familiarity with perturbation theory
  • Knowledge of wavefunction normalization techniques
  • Ability to interpret mathematical expressions in quantum physics
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  • Study the derivation of the second order correction in time-independent perturbation theory
  • Review normalization conditions in quantum mechanics
  • Explore reference texts on quantum mechanics, such as "Principles of Quantum Mechanics" by R. Shankar
  • Investigate the implications of normalization choices on quantum state calculations
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Students and researchers in quantum mechanics, particularly those focusing on perturbation theory and wavefunction analysis.

robbo96
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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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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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