Potential energy as observable

In summary, in quantum mechanics, the operator for potential energy is U, making every state an eigenstate of potential energy. However, uncertainty in potential energy is still possible due to U being a function of positions.
  • #1
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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  • #2
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.
 
  • #3
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.)
 

Related to Potential energy as observable

What is potential energy?

Potential energy is the energy that an object possesses due to its position or state. It is stored energy that has the potential to do work in the future.

How is potential energy different from kinetic energy?

Potential energy is energy that is stored, while kinetic energy is the energy of motion. Potential energy can be converted into kinetic energy when the object's position or state changes.

What are some examples of potential energy in everyday life?

Some common examples of potential energy include a stretched rubber band, a compressed spring, water at the top of a waterfall, and a book on a shelf. All of these objects have the potential to do work when their position or state changes.

How is potential energy observed and measured?

Potential energy is not directly observed since it is a state or position of an object. However, it can be calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

Can potential energy be transformed into other forms of energy?

Yes, potential energy can be transformed into other forms of energy such as kinetic energy, thermal energy, or electrical energy. This transformation occurs when the object's position or state changes, and the stored energy is released.

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