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For example: Relativistic effects are only especially prominent when approaching speeds close to that of light. But, one can take into account these effects even at low speeds and still get a correct result. Solving basic high-school kinematics problems using relativistic models would be a bit ridiculous and unnecessary--but it works.

In an analog, Quantum mechanics is used to explain and model phenomenon at an extremely small scale. What I'm wondering is, can quantum mechanics be used to explain phenomenon on a larger scale, such as Coulombic or gravitational effects?

Forgive me for my ignorance if the answer is obvious.

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Just like relativity, quantum mechanics does apply to large scale which classical mechanics applies, but it seems ridiculous as you tell what happend if we apply relativity to low speed object

Specifically,anything include frequency should have a quantum number n,where E=n*hf ,so the spring "lives"in our scale does have a quantum number n and thus get a quantized energy ,for a spring 0.1kg ,k=0.5N/m delta x =5cm ,we can find out that the frequecy is too small to get an observable energy change since the Planck constant is so small

Thus you can prove that Mawell's theory is true for Bohr model when the shell n becomes very large correspondent with the quantum physics,where Bohr also proposed a theory named correspondence priciple

And what for the object has no apparent frequecy like a moving car? Well depend on what value you desire ,maybe you can find out Ehrenfest's theorem for other thing such as potential But Bohr's correspondence principle still and as it should hold always