Can Time Be Represented as an Operator in Quantum Mechanics?

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SUMMARY

The discussion centers on the question of whether time can be represented as an operator in quantum mechanics. It concludes that there is no operator for time due to the complexities involved in relativistic quantum mechanics (QM), particularly the absence of position operators and issues with velocity operators having eigenvalues of only +c and -c. Additionally, the energy-time uncertainty principle is mentioned as a method for estimating particle decay rates, but it does not rely on a time operator. The conversation references a detailed explanation of the time-energy uncertainty principle.

PREREQUISITES
  • Relativistic Quantum Mechanics (QM)
  • Understanding of Position and Velocity Operators
  • Energy-Time Uncertainty Principle
  • Familiarity with Eigenvalues and Eigenvectors
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  • Research the implications of the absence of time operators in quantum mechanics
  • Study the relationship between position and velocity operators in relativistic QM
  • Examine the energy-time uncertainty principle in detail
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Physicists, quantum mechanics students, and researchers interested in the foundational aspects of quantum theory and the role of time in quantum systems.

arivero
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It has been asked if there exists an operator representing time. I remember some negative answers, but I do not remember the arguments.

In relativistic QM this relates to the non-existence of position operators; we are working with an (t,x,1,x2,x3) vector there. Also I believe to remember some provlem with velocity operators -its eigenvectors been only +c and -c, or so- but I am unsure about if both questions are related.

also, Energy-time indetermination is usedto estimate decay rates of particles. But there an operator is not invoked.
 
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