Is there any operator for momentum in terms of t?

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  • Thread starter Thread starter Aswin Sasikumar 1729
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Discussion Overview

The discussion revolves around the existence of a momentum operator in terms of time, similar to the energy operator represented by the Hamiltonian. Participants explore the relationship between time as a parameter in quantum theory and the operators associated with energy and momentum.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes the existence of an energy operator in terms of time and questions whether a similar momentum operator exists.
  • Another participant references the kinetic energy operator and provides a mathematical expression related to momentum.
  • A later reply emphasizes that time is treated as a parameter in quantum theory, not as an observable represented by an operator, and discusses the role of the Hamiltonian in this context.

Areas of Agreement / Disagreement

Participants express differing views on the representation of time in quantum mechanics, with some suggesting the possibility of a momentum operator in terms of time, while others assert that time is not an observable and thus cannot be represented in that way.

Contextual Notes

There is a lack of consensus on the treatment of time in quantum mechanics and its implications for defining operators related to momentum.

Aswin Sasikumar 1729
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Since there is an energy operator interms of t and a momentum operator interms of x as expected.For energy there is a hamiltanion operator interms of t which is unexpected for me.Similarly whether there is any operator interms of t for momentum also?
 
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Off the kinetic energy operator: ##2m\hat T=\hat p^2## ...
Note: the Hamiltonian operator is the energy operator.

Please provide example of "energy operator in terms of t".
 
Simon Bridge said:
Off the kinetic energy operator: ##2m\hat T=\hat p^2## ...
Note: the Hamiltonian operator is the energy operator.

Please provide example of "energy operator in terms of t".
Simon Bridge said:
Off the kinetic energy operator: ##2m\hat T=\hat p^2## ...
Note: the Hamiltonian operator is the energy operator.

Please provide example of "energy operator in terms of t".
ih/2π *∂/∂t is an operator of energy
 
This is misleading since time is a parameter in quantum theory not an observable, represented by an operator. The Hamiltonian represents the total energy of the system and is a function (or functional) of the fundamental operators of the theory's observable algebra like ##\hat{\vec{x}}## and ##\hat{\vec{p}}## for one particle in non-relativistic quantum theory ("first quantization") or the field operators in quantum field theories ("second quantization").
 

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