Download Particles and waves

QUANTUM
MECHANICS
JOURNEY TO THE WORLD OF
THE ULTRASMALL
Dr. Cyriac Mathew
Associate Professor and Department Head
Department of Chemistry
St. Albert’s College
“Quantum mechanics is the description of the
behaviour of matter in all its details and, in
particular, of the happenings on an atomic
scale. Things on a very small scale behave
like nothing you have any direct experience
about. They do not behave like waves, they
do not behave like particles, they do not
behave like clouds, or billiard balls, or weights
on springs, or like anything that you have
ever seen.”
Richard P. Feynman
Particles and waves
 Behaviour
of Particles
 Behaviour
of waves
Atomic Behaviour
 Unlike
ordinary experience
 Very difficult to get used to
 Appears peculiar and mysterious to
every one
 All direct human experience and
intuition apply to large objects.
 Even experts do not understand it
“If you are not confused by Quantum Physics then you
haven't really understood it”. N. Bohr
How to enter the world of ultra
small?
 Try
to learn about them in a sort of
abstract or imaginative fashion
 Have an idea of the relation between
Mathematics and Nature
 Don’t approach quantum mechanics
having connection with our direct
experience.
Mystery at the heart of quantum
mechanics

Mystery cannot be explained in a classical
way
 The dual nature of electrons
Behaves as a particle
Behaves as a wave
But neither
 Behave just like light
 Particle/wave nature being exhibited
depending on the type of experiment we
perform
Particle nature –
Photoelectric effect
 Wave nature –
Interference

The de Broglie Relation

All forms of matter
exhibit dual behaviour
h

mv
Heisenberg Uncertainty
Principle



The more precisely the position is determined,
the less precisely the momentum is known in
this instant, and vice versa.
--Heisenberg, uncertainty paper, 1927
The position and velocity of an object cannot be
simultaneously known with certainty.
Uncertainty Principle applies to location and
momentum along the same axis.
h
mv  x 
4
Consequences of the new
findings
 Bohr
theory ran into trouble
 Bohr tried to predict the movement of the
electrons too precisely
 Restricted electrons to certain location in
the atom
 Orbitals instead of orbits

Erwin Schrodinger came up
with a new idea.
 The famous “Schrodinger
equation”
 A mathematical equation
which provides all
information regarding an
electron in an atom.
Mathematics – The language of
Nature
 "To
those who do not know mathematics it
is difficult to get across a real feeling as to
the beauty, the deepest beauty, of nature
... If you want to learn about nature, to
appreciate nature, it is necessary to
understand the language that she speaks
in"
Richard Feynman
y = x2
x -3
y
-2.5
9
6.25
-2
4
-1.5
-1
2.25 1
0
1
1.5
2
0
1 2.25 4
2.5
3
6.25 9
9
8
6
4
2
-3
-2
-1
0
1
2
3
Schrodinger Equation
 2

 2
x
y
Hˆ   E
2
2

 2
z
2

8 2 m
h
2
E  V 
0
Hamiltonia n Operator - Operator for Total Energy
Wave Functions

Emerge as solution
to the Schrodinger
Equation
 Represented as
 A function of x, y
and z coordinates
 For convenience
we use polar
coordinates,

r ,  and 
Spherical polar coordinates
Orbitals






There are infinite number of wave functions for the
electron in the hydrogen atom.
Or an infinite number of orbitals for the electron in the
hydrogen atom.
The term atomic orbital is used for an electron wave
function since the wave function gives the maximum
possible information about electron motion in an atom
In each orbital electron has precise energy, magnitude
for angular momentum
All other dynamical variables (position, velocity etc.) do
not have sharply defined values
The square of the wave function directly gives the
position probability distribution for a particular orbit.
Quantization of energy

The permitted
values of energy
are given by
4
me
En 
2 2
80 n h
n is the Principal quantum number
Only non-zero positive integral values
Angular momentum
Quantization of angular
momentum

For a given value of
energy, the angular
momentum cannot
have any magnitude
 Known as space
quantization
h
L  l (l  1)
2
Quantum numbers
 Principal
Quantum Number
n
 Azimuthal Quantum Number
l
 Magnetic Quantum Number
m
 The quantum numbers n, l and m are
introduced in a logical way during the
process of the solution of
Schrondinger equation
Spin Quantum Number

Introduced later to
account for the
intrinsic spin of the
electron
Misleading Terms
 ‘an
electron is placed in an orbital’
 ‘an orbital is getting filled’
 ‘electrons occupy certain orbitals’
 ‘accommodate electrons in an orbital’
 ‘electrons jump from one orbital to
another,
Thank you