Why do we need perturbation theory

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SUMMARY

Perturbation theory is essential in quantum mechanics for approximating solutions to the Schrödinger equation when dealing with complex systems. Exact solutions are often unattainable, making perturbation theory a crucial method for analyzing quantum systems. This approach allows physicists to derive approximate solutions by considering small perturbations to a known solvable system, thereby facilitating the study of a wide range of quantum phenomena.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with quantum mechanics concepts
  • Knowledge of approximation methods in mathematics
  • Basic grasp of linear algebra
NEXT STEPS
  • Research the applications of perturbation theory in quantum mechanics
  • Study the differences between non-degenerate and degenerate perturbation theory
  • Explore numerical methods for solving the Schrödinger equation
  • Learn about other approximation techniques in quantum mechanics, such as the variational method
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Students and professionals in physics, particularly those specializing in quantum mechanics, as well as researchers looking to deepen their understanding of approximation methods in complex systems.

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Why do we need perturbation theory in quantum mechanics?
 
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Because solving the Schrödinger equation for the complete system in one go is too hard.
 
Most quantum systems are not exactly solvable, and perturbation theory is one very important approach to solving them approximately.
 
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