Griffiths QM Problem 2.2 Solution: Proving that Energy has to be Greater than Potential

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In this video I will show you how to solve problem 2.2 as it appears in the 3rd edition of griffiths introduction to quantum mechanics. The problem states:
Show that E must exceed the minimum value of the potential for every normalizable solution ot the time-independent Schrödinger equation. What is the classical analog to this statement?

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00 Introducing the problem
00:20 Proof
05:01 Please support my patreon!
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Love the video sir!
Please keep making these videos we really appreciate this.

abdussamifarooqui
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Your Video Helps Me Alot...
Thank You So Much Sir...
The Way You Explain...It Is So Easy To Understand...☺️

BANGATAN_ARMY_
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Wouldn't the same thing happen if E is greater than Vmax?

RishabhKhatri-rtpf
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I don't see how this is a proof, considering for instance that exp(-|x|) is also always concave up and yet it is normalizable.

Apalion