Hamiltonian Kinetic Energy Operator

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SUMMARY

The discussion centers on the confusion regarding the representation of the kinetic energy operator in quantum mechanics, specifically the use of h-bar/2m instead of p/2m. Participants clarified that h-bar (ħ) represents the reduced Planck constant, which is essential in quantum mechanics, while p denotes momentum. The kinetic energy term in the Hamiltonian is correctly expressed as ħ²/(2m) in the context of quantum mechanics, aligning with established formulations.

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  • Understanding of quantum mechanics principles
  • Familiarity with the Hamiltonian operator
  • Knowledge of the reduced Planck constant (h-bar)
  • Basic concepts of kinetic energy in physics
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Students and professionals in physics, particularly those studying quantum mechanics, as well as educators seeking to clarify concepts related to the Hamiltonian and kinetic energy in quantum systems.

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In the QM Hamiltonian, I keep seeing h-bar/2m instead of p/2m for the kinetic energy term. H-bar is not equivalent to momentum. What am I missing here?
 
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Actually, gang, I did a little more fishing and came across the answer to my question. For anyone that's interested, here's the link.

http://en.wikipedia.org/wiki/Kinetic_energy

Look under this section: Kinetic energy in quantum mechanics
 

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