How does the law of conservation of energy relate to energy transformations?
Regarding this, is energy conserved in quantum mechanics?
In general, yes. The phenomenon described by the Heisenberg uncertainty principle allows a "temporary" non-conservation of energy. The larger the amount of "non conserved" energy, the less time possible that the energy can be non conserved.
One may also ask, which equation states the law of conservation of energy?
In classical mechanics, conservation of mass and conversation of energy are considered to be two separate laws. However, in special relativity, matter may be converted into energy and vice versa, according to the famous equation E = mc2. Thus, it's more appropriate to say mass-energy is conserved.
As objects move around over time, the energy associated with them—e.g., kinetic, gravitational potential, heat—might change forms, but if energy is conserved, then the total will remain the same. Conservation of energy applies only to isolated systems.