1. Quantum mechanics
principle of uncertainty
Prepared by:
SAMAR NOURELDIN
OMER MOHAMMED
MARAM FARAH

2. Historical background of quantum
mechanics

3.  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.

4.  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

5.  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

7.  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.

8.  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

10. 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

11. • 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.

14.  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 :

16. 
2
h
tE
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:

17.  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??:

18. 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=Eb3V
8GrR7jk (April/2014).
RESONANCE/August 2013
http://www.youtube.com/watch?v=a8FTr
2qMutA (April/2014).