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[tex]\sigma x\sigma H \geq \hbar/2m |<P>|[/tex]

For stationary states this doesn't tell you much -- why not??

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- Thread starter ttiger654
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- #1

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[tex]\sigma x\sigma H \geq \hbar/2m |<P>|[/tex]

For stationary states this doesn't tell you much -- why not??

- #2

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- #3

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[tex]\sigma x\sigma H \geq \hbar/2m |<P>|[/tex]

For stationary states this doesn't tell you much -- why not??

solution-

[x,p2/2m+V]=1/2m[x, p2]+[x,V];

[x, p2]= xp2 − p2x = xp2 − pxp + pxp − p2x = [x, p]p + p[x, p].

using the equation [x,p]=ih{this is known as canonocal commutation relation}

[x, p2]= ihp + pih = 2ihp. and And [x, V ] = 0,

so [x,p2/2m+ V]=1/2m(2ihp) = ihp/m

The generalized uncertainty principle says, in this case,

σ2xσ2H≥{(1/2i)(ih/m)<p>}^2={h/2m<p>}^2⇒ σxσH ≥h/2m|<p>|. QED

For stationary states σH = 0 and p = 0, so it just says 0 ≥ 0.

- #4

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for reference u can use {griffiths_d.j._introduction_to_quantum_mechanics__2ed.}

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