How to fit quantum LHO into quantum mechanics?

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SUMMARY

The discussion centers on the relationship between the energy equations in quantum mechanics, specifically addressing the quantum linear harmonic oscillator (LHO). The equation E=n*h*v(nu) is contrasted with the correct energy expression for the LHO, E=(n+1/2)h*v. The discrepancy arises when using ladder operators, which may overlook the 1/2 term. The correct understanding of these equations is crucial for grasping quantum mechanics principles.

PREREQUISITES
  • Understanding of quantum mechanics fundamentals
  • Familiarity with the quantum linear harmonic oscillator model
  • Knowledge of ladder operators in quantum mechanics
  • Basic grasp of differential equations related to quantum systems
NEXT STEPS
  • Study the derivation of the quantum linear harmonic oscillator energy levels
  • Learn about ladder operators and their application in quantum mechanics
  • Explore the implications of the zero-point energy represented by the 1/2 term
  • Investigate the general principles of quantum mechanics related to energy quantization
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Students and researchers in physics, particularly those focusing on quantum mechanics, as well as educators seeking to clarify concepts related to the quantum linear harmonic oscillator.

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Can anyone help me with this?
The basic equation in quantum mechanics says that E=n*h*v(nu) where n = 1,2,3,...
How is then possible that the quantum linear harmonic oscillator has an energy E=(n+1/2)h*v? If someone can explain this, please help
 
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The second equation is correct. If you solve the differential equation for the harmonic oscillator, that's what you get.

If you instead use ladder operators, then maybe you miss out on the 1/2 term, so that's why you got the 1st equation instead. I'm not sure how you are supposed to get the 1/2 term with ladder operators.
 
I'm just guessing that what you mean by the first equation should be some "general QM principle"(?)
[tex]\Delta E= h\nu[/tex].

Indeed the second equation is correct for a harmonic oscillator.
 

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