Ppt for better understanding

1. Heisenberg's Uncertainty
Principle
Understanding the Fundamental
Limit of Measurement in Quantum
Mechanics

2. Introduction
• The Uncertainty Principle states that it is
impossible to simultaneously measure the
exact position and momentum of a particle
with perfect accuracy.

3. Mathematical Form
• The principle is mathematically expressed as:
• Δx * Δp ≥ /2
ℏ
• Where:
• Δx = Uncertainty in position
• Δp = Uncertainty in momentum
• ℏ = Reduced Planck's constant (h/2π)

5. Explanation
• When we try to measure a particle's position
more accurately, its momentum becomes
more uncertain, and vice versa. This is a
fundamental property of quantum systems,
not a limitation of measurement technology.

6. Real-World Examples
• 1. Electron Microscopes: Higher resolution
means higher energy electrons, making precise
position determination harder.
• 2. Quantum Tunneling: Particles can pass
through barriers due to uncertainty in energy
and time.
• 3. Atomic and Molecular Physics: Defines limits
in spectroscopy and atomic structure
calculations.

7. Conclusion
• The Uncertainty Principle is a cornerstone of
quantum mechanics. It explains why classical
physics cannot describe atomic and subatomic
systems accurately and has profound
implications in science and technology.