
A physical system is symmetric if after any change, the system is exactly the same as it was before. The change is called a symmetric transformation and we say that the system is invariant under the transformation. In 1915, the great mathematician Emmy Noether showed that any law of symmetry, in both classical and quantum mechanics, originates a conservation property. The Noether’s theorem says: If Euler-Lagrange’s equations are invariant under any transformation of coordinates then there is a conservative integral of motion and something is conserved.
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