Understanding the Relationship Between H^DaggerH and Dual Spaces

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SUMMARY

The discussion centers on the relationship between the operator H^†H and dual vector spaces in quantum mechanics. It is established that H^†, the adjoint of the Hamiltonian operator H, is inherently linked to H, as both are Hermitian operators. The inquiry clarifies that H^†H does not exist independently of H, emphasizing their interdependence in the context of quantum mechanics and linear algebra.

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  • Understanding of Hermitian operators in quantum mechanics
  • Familiarity with dual vector spaces and their properties
  • Basic knowledge of linear algebra concepts
  • Concept of adjoint operators in functional analysis
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lonewolf219
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Hi,

I have a related question to one I just posted:

Is H^DaggerH a dual vector space, or perhaps a dual vector field? Could H^dagger exist independently of H, or are they considered a kind of pair?
 
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The Hamiltonian is a Hermitian operator, so by definition [itex]H^{\dagger} = H[/itex].
 
Thanks, dipole... My question is probably not a very good one!
 

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