(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let's say T is kinetic energy and V is Potential.

Then, find a principle between T and V by using

dA^2dB^2 (larger or equal) {(1/2i)(<[A,B]>)}^2

3. The attempt at a solution

First I try to find commutator of T and V, [T,V]

then it gives little bit dirty expression..

[T,V] = -(h^2/2m) [ (d/dx)^2(V) + 2(d/dx)V(d/dx) ]

(Here h represents h over 2pi)

Then when I plug it into the general uncertainty principle,

i on the principle does not cancel out.

so the inequality cannot hold.

I thought that mathematically the second deravative of V(x) must be zero to fit the principle

but there is no clue. Maybe it is wrong also.

I can't go on further..

What did I wrong?

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# Homework Help: Uncertainty principle between Kinetic energy and Potential energy

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