Can quantum mechanics be derived from deeper principles?

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Can quantum mechanics be derived from deeper principles?

For example, special relativity results directly from the fact that the speed of light is the same for all reference frames. Conservation laws of momentum and energy come from certain symmetries of space and time.

Does quantum mechanics result from some symmetry or from some deeper law of nature? Can Schrödinger's Equation be derived theoretically from a deeper principle?
 
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