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Heisenberg's Uncertainty Principle

by eehiram
Tags: heisenberg, principle, uncertainty
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Dec14-13, 11:26 AM
P: 121
My source is the high school chemistry textbook:
General Chemistry, 2nd Edition, by Donald A. McQuarrie and Peter A. Rock, published 1987
(This is not for a high school homework assignment.)

According to Heisenberg's Uncertainty Principle, the product of the uncertainty in the momentum measurement Δp and the uncertainty in the position measurement Δq of a particle is greater than or equal to Planck's constant h divided by 4[itex]\pi[/itex]:

Δp Δq ≥ h / (4[itex]\pi[/itex])

This is not due to poor measurement or poor experimental technique, as is sometimes supposed: that bouncing waves or particles affects the location of the particle being measured, like in a billiard collision. (The measurement waves or particles are presumed to be of comparable size to the particle being measured.)

Heisenberg's Uncertainty Principle is usually limited to only small particles.

Does this mean that particles do not have a physical location unless and until we observe them?

(I do not want to make a broad question, but rather a narrow question.)

Does Heisenberg's Uncertainty Principle necessarily pit Classical physics (and Logic and common sense and billiards) against the Copenhagen School?

Has Heisenberg's Uncertainty Principle agreed with the majority of experimental laboratory results?
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Dec14-13, 01:42 PM
PF Gold
phinds's Avatar
P: 6,364
The HUP is trivially easy to demonstrate experimentally and there are no results that disagree with it. If there were, it would have been invalidated. That's how science works.

There are MANY discussions about HUP on this forum if you want more details. You are correct about it being a fundamental fact of nature, not having anything to do with our measurement capabilities.
Dec14-13, 02:51 PM
Sci Advisor
PF Gold
dlgoff's Avatar
P: 2,726
Quote Quote by ZapperZ's physics blog
The HUP isn't about a single measurement and what can be obtained out of that single measurement. It is about how well we can predict subsequent measurements given the identical conditions.

Dec14-13, 04:15 PM
P: 121
Heisenberg's Uncertainty Principle

Thanks for the responses and the link. I may have to make a more specific, narrow question about a particular aspect of HUP. I'll try to come up with something later.

I see on ZapperZ's physics blog that the width of the slit can be compared to the de Broglie wavelength of the particle (or in the case of light, the wavelength) passing through the slit. When the width becomes smaller than the de Broglie wavelength, then the quantum effect of the single slit diffraction pattern takes hold: the spread of the particles being detected starts expanding; the "Gaussian spread" becomes fatter and fatter. (This is from the 3rd to last paragraph, starting with "It gets interesting as you decrease the slit.")
Dec14-13, 05:59 PM
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HW Helper
P: 11,928
Perhaps one may enlighten me on the occurence of 'Heisenberg's Uncertainty' in Chemistry as a whole, and in elementary (i.e. high-school) chemistry in particular...
Dec15-13, 02:41 AM
Borek's Avatar
P: 23,600
Typically it is just mentioned as a part of intro to quantum chemistry. Intro doesn't say a word about math, just says electrons are on orbitals, what kinds of orbitals are there, how they are described by quantum numbers, how they are filled. Not mentioning HUP won't change the general picture as shown, as it is not used for anything, more like added as a random fact.

Dec15-13, 09:50 AM
P: 121
Again, the textbook from 1987 is:
General Chemistry, 2nd Ed., by Donald A. McQuarrie and Peter A. Rock

Proceeding somewhat historically, first a non-quantum chemistry is presented:

Chapter 1: Atoms and Molecules
Includes Elements, Metals and Nonmetals, Dalton's Atomic Theory, Molecules, etcetera

Interchapter A: Separation of Mixtures

Chapter 2: Chemical Reactions and the Periodic Table
Includes Group Properties, Periodicity, Periodic Table, Groups of Elements, etcetera

Interchapter B: The Alkali Metals

Chapter 3: Chemical Calculations
Includes Mole, Avogadro's Number, Stoichiometry, etcetera

Interchapter C: The Main Group Metals

Chapter 4: The Properties of Gases
Includes Boyle's Law, Charles' Law, Avogadro's Law, Ideal-Gas Equation

Interchapter D: Hydrogen and Oxygen

Chapter 5: Thermochemistry
Includes 1st Law of Thermodynamics, Chemical Reactions and Heat, Enthalpy Changes, etcetera

Interchapter E: Energy Utilization


After this historical non-quantum chemistry is presented, the textbook then pivots to quantum chemistry in chapter 6:

Chapter 6: The Quantum Theory and Atomic Structure
Includes 1st Ionization Energies, Ionizations Energies and Periodicity, Electromagnetic Spectrum, Line Spectra, Photons, Photoelectric Effect, De Broglie Wavelength, Electron Microscope, Quantization, Electronic transitions, Heisenberg Uncertainty Principle, etcetera

In the margins, some brief biographies are provided of early 1900s quantum pioneers:
Max Planck, Albert Einstein, Louis de Broglie, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Wolfgang Pauli. The remaining chapters (up to chapter 24 and interchapter N) derive from a foundation of quantum chemistry.

Thank you for your inquiry.

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