Heisenberg uncertainty principle

A short form presentation on heisenberg uncertainty principle.that what this principle tells us basically.

1. Heisenberg Uncertainty Principle Rana Muhammad Aqib Altaf ID # F2017139002 [email protected]

2. Contents INTRODUCTION DEFINITION WHAT IS POSITION? WHAT IS MOMENTUM? RELATIONSHIP B/W POSITION AND MOMENTUM ENERGY TIME RELATION EXAMPLE

3. INTRODUCTION Uncertainty principle was stated by Werner Karl Heisenberg in 1927 . This principle gives a very vital relation between momentum and position of an object.

4. Definition IN QUANTUM PHYSICS… A particle is described by a wave. Position - Where the wave is concentrated Momentum - The wave length The position is uncertain to the degree that the wave is spread out. The momentum is uncertain to the degree that the wavelength is unclear.

5. POSITION ( Δ x) When is it certain ? This means that position is uncertain for conditions opposite to those mentioned above NARROW wave group GREATER Range of λ WELL DEFINED Position

6. MOMENTUM ( Δ p) When is it certain ? This means that momentum is uncertain for conditions opposite to those mentioned above. WIDE WAVE GROUP WELL DEFINED λ MORE PRECISE Momentum

7. Position-Momentum Relation Position-Momentum Relation- can be precisely derived from the Schrodinger equation. x - the uncertainty in the x-coordinate of the position of an object. P - the uncertainty in the x-component of the momentum of that object. h- Planck’s constant.  

8. Energy and Time Another pair of quantities that follow the uncertainty principle Energy may be in the form of EM waves, so the limited time available restricts the accuracy with which Frequency of the waves can be determined. Δ E Δ t ≥ ħ⁄2

9. Continue….. The more accurately we know the energy of a body, the less accurately we know how long it possessed that energy The energy can be known with perfect precision (∆ E = 0 ), only if the measurement is made over an infinite period of time (∆ t = ∞)

10. Implications It is impossible to know both the position and momentum exactly, i.e., x =0 and p =0 . These uncertainties are inherent in the physical world and have nothing to do with the skill of the observer. Because h is so small, these uncertainties are not observable in normal everyday situations  

11. Example: A pitcher throws a 0.1-kg baseball at 40 m/s So momentum is 0.1 x 40 = 4 kg m/s Suppose the momentum is measured to an accuracy of 1 percent , i.e., p = 0.01 p = 4 x 10-2 kg m/s  

12. Continued…. The uncertainty in position is then m No wonder one does not observe the effects of the uncertainty principle in everyday life!