Quantum mechanicsprinciple of uncertainty

Prepared by:SAMAR NOURELDINOMER MOHAMMEDMARAM FARAH

Historical background of quantum mechanics

In the 17th century, Isaac Newton decided in favour of a

particle theory.

Around the same time, Huygens developed a wave theory Much later (about 1800), the wave model of light gained strong experimental support from the work of Thomas Young.

There were two serious difficulties with Newton’s particle theory. It failed to explain :

the fact that when a beam of light passes from one medium to another, some of it is reflected and some of it is refracted. 

the phenomena of interference and diffraction.

Albert Einstein wrote “When a light ray spreads out from a point source, the energy is not distributed continuously over an increasing volume [wave theory of light], but consists of a finite number of energy quanta that are localized at points in space, move without dividing, and can only be absorbed or generated as complete units.” Einstein used the term light quantum.

After conducting many experiments they discovered the light behaves like wave and particle at the same time call this the wave-particle duality of light .

in 1923 De Broglie, a Ph.D. student at the University of Paris , felt that if radiation exhibits wave-particle duality, matter should have a dual nature too!!

This was confirmed using a double-slit experiment with particles of matter, such as electrons

Every material particle has wave properties with a wavelength equal to:

= h/ms (De Broglie) m: mass of particle s: its speed h: Planck’s constant

If the particle size is less than the De Broglie wavelength of the electrons, the charge carriers may be treated quantum mechanically as where the size of the box is given by the dimensions of the crystallites.

"particles in a box

De Broglie wavelength or Heisen-berg's

uncertainty principle formalism

 In quantum mechanics, everything moves as a wave but exchanges energy and momentum as a particle.

E = hf         p = h/λ

• It is even possible to observe the wave nature of larger objects such as atoms and molecules.

The uncertainty principle applies to all waves: water waves, light, sound, and the matter waves described by quantum mechanics.

an electron will used as an example here.

While an electron is moving, don't think of it as a particle that follows a particular path through space.

Electron wave

Position/momentum Relation

Relation statement:

• product of the variance in the width of a pulse Δx = √<x²> - <x>² times the variance in the wave numbers in the pulse Δk = √<k²> - <k>² must be greater than or equal to 0.5.

 wave number is k = 2π/λ

•So, We can say:The narrower the wave pulse is in position, the more wavelengths are needed to describe it.

ΔxΔk ≥ 0.5

• In quantum mechanics it is common to multiply both sides of this equation by h/(2π).

 hk/(2π)=P

So the equation become:

And the statement become:it is impossible to know the position and the momentum of a particle simultaneously.

Helps determine the size of electron clouds, and hence the size of atoms.

This concept is being used to predict & evaluate the quantum confinement regime “which is resulting from Quantum size effect”.

What this relation make us know??:

the diameter calculated using the uncertainty principle is:(1/2) the thermal de Broglie wavelength of

the electron/hole.

quantum confinement will be effective when :

Energy/Time Relation

2

htE

When the energy is transferred to electron “or other object” over a time t , the smaller the time interval, the greater the uncertainty in Energy.

t= time interval that the system remains in a given energy state.

Relation statement:

this relation means that conservation of energy can be violated if the time is short enough.

The existence of a Zero-Point –Energy: vibrational energy cannot be zero even at T=0K is also a consequence of the Heisenberg principle. If the vibration would cease at T=0K, then the position and momentum would both be 0, violating the HUP.

It is possible that empty space locally does not have zero energy but may actually have sufficient E for a very short time t to create particles and their antiparticles.

What this relation make us know??:

References:

NaNo The essentials[understanding Nanoscience and Nanotechnology]/proffessor:Indian Istitute of technology, Madras/Mc Groe-Hill

http://lamp.tu-graz.ac.at/~hadley/nanoscience/week2/2.html

(April/2014).

Quantum mechanics/Dr. Marc Madou Chancellor’s Professor UC Irvine 2012

http://www.youtube.com/watch?v=Eb3V8GrR7jk

(April/2014).

RESONANCE/August 2013

http://www.youtube.com/watch?v=a8FTr2qMutA

(April/2014).

Questions ??

Feynman said, "I think I can safely say that nobody understands quantum mechanics."