Raising and Lowering Operators

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SUMMARY

The discussion centers on the concept of raising and lowering operators as presented in Griffith and Shankar's texts. These operators are essential in quantum mechanics, particularly for the harmonic oscillator and angular-momentum eigenstates, which are linked through the SU(N) symmetry of the N-dimensional symmetric harmonic oscillator. The participants explore the origins and applications of these operators, emphasizing their role in both one-dimensional and multi-dimensional systems.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with harmonic oscillator models
  • Knowledge of angular momentum in quantum systems
  • Basic concepts of SU(N) symmetry
NEXT STEPS
  • Study the mathematical derivation of raising and lowering operators in quantum mechanics
  • Explore the applications of SU(N) symmetry in quantum field theory
  • Learn about the role of raising and lowering operators in quantum harmonic oscillators
  • Investigate the relationship between angular momentum and raising/lowering operators
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Students and professionals in physics, particularly those specializing in quantum mechanics, quantum field theory, and mathematical physics will benefit from this discussion.

jjohnson
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In Griffith and Shankar, the raising and lowering operator seem to appear from nowhere, but it seems really elegant.

Where do they come from, is it some corollary from certain mathematical structure?

Can anyone give a brief explanation?
 
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In which context? There are lowering and raising operators for the harmonic oscillator, angular-momentum eigenstates (closely related by the way due to the SU(N) symmetry of the N-dimensional symmetric harmonic oscillator) and for free-particle modes in QFT.
 
Thank you for replying.
So for harmonic oscillator, all dimensions are separable (H = Hx+Hy+Hz), does it depend on dimensionality? Even for one-dimensional harmonic oscillator, we can use raising and lowering operators.

Thanks
 

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