Exploring the Uncertainty Principle: Solving Homework Problems

In summary, the Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental principle in quantum mechanics proposed by German physicist Werner Heisenberg in 1927. It states that there is a limit to the precision with which certain pairs of physical properties of a particle can be known simultaneously. This challenges the traditional idea of determinism and has implications for our understanding of the physical world. Some real-world applications of the Uncertainty Principle include quantum cryptography and the development of quantum computing. While it is widely accepted in the scientific community, it is still considered a theory and has not been definitively proven to be true.
  • #1
bon
559
0

Homework Statement


See q attached



Homework Equations





The Attempt at a Solution



Am i right in thinking that the answer to both questions is yes? Neither of the commutators [p, V(x)] nor [x, H = + or - ih..

therefore is the answer to both a and b yes?
 

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  • #2
The thing is that [p, V(x)] gives -ih/2pi DV/DX where D/Dx is partial d/dx..

does the uncertainty principle only hold between oberservables whose commutator = plus or minus ih /2pi?

Thanks
 
  • #3
Can anyone help with this?
 

Related to Exploring the Uncertainty Principle: Solving Homework Problems

What is the Uncertainty Principle?

The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental principle in quantum mechanics that states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known simultaneously.

Who discovered the Uncertainty Principle?

The Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927. He presented the idea as part of his uncertainty relations, which were a set of mathematical equations that explained the limitations of measuring certain properties of quantum particles.

How does the Uncertainty Principle affect our understanding of the physical world?

The Uncertainty Principle has significant implications for our understanding of the physical world. It suggests that at the quantum level, the behavior of particles is inherently unpredictable, and that we can never know everything about a particle's state at any given time. This challenges the traditional idea of determinism, which suggests that the future can be predicted from the past with complete accuracy.

What are some real-world applications of the Uncertainty Principle?

The Uncertainty Principle has been applied in many areas of science and technology, including quantum cryptography, where it is used to create secure communication systems. It also plays a crucial role in the development of quantum computing, as it sets limitations on the precision of measurements and calculations at the quantum level.

Is the Uncertainty Principle a proven fact?

While the Uncertainty Principle has been supported by numerous experiments and is widely accepted in the scientific community, it is still considered a theory. This means that it is based on observations and mathematical models, but it has not been definitively proven to be true. However, the Uncertainty Principle has been a fundamental principle in quantum mechanics for over 90 years and has been consistently supported by experimental evidence.

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