I Why is the minimum energy equal to the energy uncertainty?

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Why is the minimum energy equal to the energy uncertainty?
I was watching this video on Youtube, however, I don't get the step at 14:50 where he says that ΔE≥½hf means that E0=½hf.

Could someone explain why the minimum energy is equal to the energy uncertainty?

 
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"Watch this obviously confusing video and then explain it to me" is a big, big ask.
asdf said:
Could someone explain why the minimum energy is equal to the energy uncertainty?
It's not.
 
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Amended: "Watch this obviously confusing 37 minute video..."
 
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asdf said:
I don't get the step at 14:50 where he says that ΔE≥½hf means that E0=½hf.
It's just saying that, since the energy of any state whatever must be greater than or equal to ##hf / 2##, the energy of the lowest energy state, the ground state energy ##E_0##, is equal to ##hf / 2##.

asdf said:
Could someone explain why the minimum energy is equal to the energy uncertainty?
That's not what the above is saying.
 
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