Time in Quantum Mechanics

Time in Quantum Mechanics

1. Arrival Time

   • Aharanov-Bohm
     • Concerned with interpretations of time energy uncertainty relation. Suggested that proper interpretation required operator formalism for time. Created time operator for arrival time problem that was self-adjoint. Does it give the proper time of arrival distribution? Question for experiment?
   • Kijowski
     • Analysed axiomatically the properties of a time of arrival distribution. Constructed appropriate time of arrival POVM. 
   • Grot-Tate
     • Created appropriated TOA operator through regularization technique. Argued space-time equivlance in QM same as in classical mechanics. 
   • Allcock1
     • Showed difficulties with constructing normalised time states. Created states in extended energy domain by modelling particle with source
   • Muga Leavens
     • Reviewed TOA approaches, emphasized importance of Allcock's work. 
     • Commented on interpretation of non-orthogonal TOA eigenstates

2. Time-Energy Uncertainty

   • Aharanov Bohm
     • Concerned with interpretations of time energy uncertainty relation. Suggested that proper interpretation required operator formalism for time. Created time operator for arrival time problem that was self-adjoint. Does it give the proper time of arrival distribution? Question for experiment?
   • Giannitrapani
     • Allowed assosciation of Time observable with POVM in generalised observable scheme. Considered quantum clock of dynamical variable treatment time of free particle in 1D. Showed consistency with uncertainty principl

3. Characteristic Time

   • Smith
     • Argued that the lifetime of metastable states undergoing scattering (collision time) could be be found for single energies. Did so using a lifetime matrix.

4. Von Neumann

   • Formalised mathematical principles of QM including second postulate

5. Backflow

   • Muga-Palao-Leavens
     • Discussed measurement of TOA distribution and detector model. 

6. Quantum Zeno

   • Sudarshan-Misra
     • Supported allcocks pessimism over TOA by disallowing continuous measurements without the prevention of transition (zeno effect)

7. Time Operators

   • Giannitrapani
     • Allowed assosciation of Time observable with POVM in generalised observable scheme. Considered quantum clock of dynamical variable treatment time of free particle in 1D. Showed consistency with uncertainty principl
   • Muga-Palao-Leavens
     • Tried to interpret TOA eigenstates by writing in coordinate representation. Showed that Muga delgado and grot tate's work in making self adjoint versions is not that useful.