Is there any operator for momentum in terms of t?

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SUMMARY

The discussion centers on the existence of a momentum operator in terms of time (t) within quantum mechanics. It establishes that while there is a Hamiltonian operator representing energy in terms of time, time itself is not treated as an observable in quantum theory. The kinetic energy operator is defined as 2m𝛤T = 𝛤p², and the energy operator is represented by ih/2π * ∂/∂t. The Hamiltonian operator encapsulates the total energy of a system and is dependent on the fundamental operators of the observable algebra.

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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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