Uncertainty Principle textbook equation

In summary, the conversation discusses the Heisenberg uncertainty principle for position and momentum as written in a Physics textbook. The individual is confused about the value of ΔxΔp, with the textbook stating ΔxΔp ≥ h-bar and other sources stating it as ΔxΔp ≥ (h-bar)/2. It is clarified that the latter is correct when interpreting Δx and Δp as standard deviations, but the textbook may be wrong. The expert mentions that when dealing with order-of-magnitude estimates, a factor of 2 or 1/2 does not significantly affect the result. The correct Heisenberg-Robertson uncertainty relation is ΔxΔp ≥ (h-bar)/2, and the
  • #1
Daniel1992
22
0
I have been going through my Physics textbook to brush up on my Quantum Mechanics before starting my next QM course next academic year and the Heisenberg uncertainty principle for position and momentum is written as ΔxΔp ≥ h-bar when I thought it was ΔxΔp ≥ (h-bar)/2. Other sources say it is the latter so am I missing something? Or is the textbook just wrong?
 
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  • #2
The latter (hbar/2), assuming that Δx and Δp are interpreted as standard deviations from their respective means.
 
  • #3
So are there circumstances when ΔxΔp ≥ h-bar is correct? Say when you are not dealing with standard deviations?
 
  • #4
When you're interested mainly in order-of-magnitude estimates (powers of ten), a factor of 2 or 1/2 or something like that doesn't affect the result significantly.
 
  • #5
The correct Heisenberg-Robertson uncertainty relation is
[tex]\Delta x \Delta p \geq \frac{\hbar}{2}.[/tex]
You can show that the Gaussian wave packets are the only ones, where the equality sign is valid.
 
  • #6
OK, thanks for clearing that up.
 

1. What is the Uncertainty Principle textbook equation?

The Uncertainty Principle textbook equation, also known as the Heisenberg Uncertainty Principle, is a fundamental equation in quantum mechanics that describes the relationship between the position and momentum of a particle. It states that the more precisely one of these quantities is known, the less precisely the other can be known.

2. Who developed the Uncertainty Principle textbook equation?

The Uncertainty Principle textbook equation was developed by German physicist Werner Heisenberg in 1927. Heisenberg's work was a major breakthrough in quantum mechanics and earned him the Nobel Prize in Physics in 1932.

3. What is the significance of the Uncertainty Principle textbook equation?

The Uncertainty Principle textbook equation has significant implications for our understanding of the physical world. It shows that there is a fundamental limit to the precision with which we can measure certain properties of particles. This has led to the development of new theories and technologies in fields such as quantum computing and cryptography.

4. How is the Uncertainty Principle textbook equation used in practical applications?

The Uncertainty Principle textbook equation is used in a variety of practical applications in fields such as physics, chemistry, and engineering. For example, it is used in the design of electron microscopes and other high-precision instruments, and in the development of quantum-based technologies such as atomic clocks and sensors.

5. Is the Uncertainty Principle textbook equation universally accepted?

While the Uncertainty Principle textbook equation is a well-established principle in quantum mechanics, there have been ongoing debates and discussions about its interpretation and applicability in different scenarios. Some physicists have proposed alternative theories that challenge the principle, but it remains a fundamental concept in modern physics.

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