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## Main Question or Discussion Point

I was going through Le Bellac's Quantum Physics book.In the "symmetry" chapter 1st page(Classical physics), he makes the following comments a part of which look a bit weired to me...Each statement starts with "Invariance of the potential energy".Do you think this is meaningful?

*Invariance of the potential energy under time-translations implies conservation of mechanical energy E = K + V , the sum of the kinetic energy K and the potential energy V .

*Invariance of the potential energy under spatial translations parallel to a vector n implies conservation of the momentum component p_n .

*Invariance of the potential energy under rotations about an axis n implies conservation of the component j_n of the angular momentum.

*Invariance of the potential energy under time-translations implies conservation of mechanical energy E = K + V , the sum of the kinetic energy K and the potential energy V .

*Invariance of the potential energy under spatial translations parallel to a vector n implies conservation of the momentum component p_n .

*Invariance of the potential energy under rotations about an axis n implies conservation of the component j_n of the angular momentum.