## h/4pi in Heisenberg's Indeterminacy Equation

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Matthew Gutierrez 2D
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Joined: Fri Sep 25, 2015 3:00 am

### h/4pi in Heisenberg's Indeterminacy Equation

What does the $\frac{h}{4\pi }$ in the equation represent and why does it have to be less than or equal to the product of $\Delta x\Delta p$? Was this value arbitrarily chosen for the inequality or was it actually experimentally determined?

Shelby Yee 1J
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Joined: Fri Sep 25, 2015 3:00 am

### Re: h/4pi in Heisenberg's Indeterminacy Equation

h/4pi is an experimentally determined constant. Basically, it exists to show that there is a limit to the certainty to which you can know the position and the momentum of the particle simultaneously.

Lillian Xie 1K
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Joined: Fri Sep 25, 2015 3:00 am

### Re: h/4pi in Heisenberg's Indeterminacy Equation

Adding on to what Shelby said, it makes sense that $4\pi$ would be the constant that was experimentally derived because it relates back to how most graphs of waves involve the sine curve, which can be more conveniently graphed with a constant involving $\pi$.

Chem_Mod
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### Re: h/4pi in Heisenberg's Indeterminacy Equation

The constraining constant in Heisenberg's indeterminacy equation comes from theoretical models. Although there have been experimental verifications, the original discovery of the relation came when using the Schrodinger equations.

The origin of that property is based on the double slit experiment for the electron which is described in the textbook. The number itself is a consequence of light having discrete states and, since light is the smallest "particle" we consider and measure in quantum mechanics, we measure most quantities in terms of h.

The 1/4*pi is due to the dispersion of a given "wavepacket" or photon. Dispersion is a measure of how blurry something is, where we model the photon as a gaussian or more commonly known as a bell curve that has width 1/4*pi.