Potential energy as observable

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SUMMARY

The operator for potential energy in quantum mechanics is denoted as U, indicating that every state is an eigenstate of potential energy, resulting in no uncertainty regarding its value. Although potential energy is a component of the Hamiltonian, it can be rendered self-adjoint, yet it typically does not share eigenstates with the entire Hamiltonian. Consequently, the concept of uncertainty in potential energy is rendered meaningless, as it is inherently linked to the positions that define U.

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  • Understanding of quantum mechanics principles
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  • Knowledge of eigenstates and eigenvalues
  • Concept of self-adjoint operators in quantum theory
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  • Study the role of the Hamiltonian in quantum systems
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Quantum physicists, students of quantum mechanics, and researchers interested in the mathematical foundations of potential energy and its implications in quantum systems.

AlonsoMcLaren
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In quantum mechanics it seems that the operator for potential energy is U. Therefore, every state is an eigenstate of potential energy and there will never be any uncertainty in potential energy? It seems weird...
 
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The potential energy is only part of the whole Hamiltonian. It can be rendered self-adjoint but typically won't share eigenstates with the whole Hamiltonian, so any 'uncertainty' for it is a meaningless concept.
 
AlonsoMcLaren said:
In quantum mechanics it seems that the operator for potential energy is U. Therefore, every state is an eigenstate of potential energy and there will never be any uncertainty in potential energy? It seems weird...

U is a function of the positions, hence it inherits its uncertainty from these.
(It doesn't matter that U is only part of the Hamiltonian.)
 

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