Is energy quantized?

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Is energy quantized?
 

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Energy transfer in the form of EM waves is quantized. But I don't believe energy as a whole is. I'm pretty sure I can transfer any amount of kinetic energy to an object.
 
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For a free particle moving in a one dimension in the interval (-infty, +infty) its energy can take any possible value.
 
You might want to read https://www.physicsforums.com/blog.php?b=3588
 
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