A Pointed Weak Energy Conservation Law via Noether's Theorem


  • Allen Parks Retired US navy research scientist




Noether's Theorem, Conservation Law, Pointed weak energy


Noether’s theorem is used to identify a conservation law for the quantum mechanical pointed weak energy. Under this law the pointed weak energy is a constant of the motion and leads to simple expressions for the correlation amplitude between and probability for an associated evolving quantum state and the state at a previous initial time.



Aharonov, Y. and L. Vaidman. 1990. Propertie of a quantum system during the interval between two measurements. Phys. Rev. A. 41(1): 11-20.

DOI: 10.1103/PhysRevA.41.11

Aharonov, Y. D. Albert, A. Casher, and L. Vaidman. 1986. Novel properties of preselected and postselected ensembles in D. Greenberger (ed.), New Techniques and Ideas in Quantum Measurement Theory, pp. 417-421. New York Academy of Science.

Aharonov, Y., D. Albert, and L. Vaidman. 1988. How the result of a measurement of a component of the spin of a spin-1⁄2 particle can turn out to be 100. Phys. Lett. 60: 1351-1354.

DOI: 10.1103/PhysRevLett.60.1351

Parks, A. D. 2014. Weak energy: form and function in D. Strupa and J. Tollaksen (eds.), Quantum Theory: A Two-Time Success Story, pp. 291-302. Yakir Aharonov Festschrift. Springer Milan.

Parks, A. D. 2006. Pointed weak energy and quantum state evolution in Pancharatnam-Fubini-Study configuration space. J. Phys. A.: Math. Gen. 39: 601-615.

DOI: 10.1088/0305-4470/39/3/012

Parks, A. D. 2007. Pointed weak energy and quantum geometric phase. J. Phys. A: Math. Theor. 40: 2137-2146.

DOI: 10.1088/1751-2113/40/8/018

Neuenschwander, D. 2011. Emmy Noether’s Wonderful Theorem. Johns Hopkins Univ. Press. Baltimore.

Parks, A. D. 2003. A weak energy stationary action principle for quantum state evolution. J. Phys. A: Math. Gen. 36: 7185-7192.

DOI: 10.1088/0305-4470/36/25/318




How to Cite

Parks, A. (2023). A Pointed Weak Energy Conservation Law via Noether’s Theorem. Proceedings of the West Virginia Academy of Science, 95(3). https://doi.org/10.55632/pwvas.v95i3.1020



Research Articles