L1.3 Calculating the energy corrections | Summary and Q&A

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February 14, 2019
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L1.3 Calculating the energy corrections

TL;DR

The energy corrections in perturbation theory can be calculated by finding the expectation value of the perturbation in the unperturbed state.

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Questions & Answers

Q: How is the left-hand side of the equation zero in perturbation theory?

The left-hand side of the equation is zero because the eigenstate equation evaluates to zero, simplifying the calculation of the energy correction.

Q: How can the first correction to the energy be calculated?

The first correction to the energy can be obtained by finding the expectation value of the perturbation operator in the unperturbed state, without needing to know how the state changes.

Q: What is the significance of the generalization formula in perturbation theory?

The generalization formula allows for calculating higher-order corrections to the energy by knowing the previous correction, providing a systematic approach to analyzing perturbed systems.

Q: How does the generalization formula relate to the first correction in perturbation theory?

The generalization formula builds upon the concept of the first correction, stating that the kth order energy correction can be determined if the (k-1)th correction to the state is known.

Summary & Key Takeaways

  • The left-hand side of the equation is zero because the eigenstate equation evaluates to zero. The right-hand side is a number representing the expectation value of the perturbation operator.

  • The first correction to the energy can be obtained by calculating the expectation value of the perturbation in the unperturbed state without needing to know how the state changes.

  • The generalization of the formula involves calculating higher-order corrections to the energy by knowing the previous correction.

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