PH-1001 (Physics-1)
Dr. A. K. Singh
Department of Physics & Astronomy
National Institute of Technology
Rourkela-769008
Time Table
Monday Wednesday Thursday Friday
8:00 -8:55 AM 4:15 - 3:10 PM 10:00-10:55 AM 9:00-9:55 AM
Section A
Time Slot: TA
2
Topics
Special Relativity, Particle properties of Waves,
Wave properties of Particles, Quantum Mechanics.
Mark Distributions: GRADE Distributions:
End Term: 80% 90 Ex
TA: 20% 80 A
70 B
60 C
TA: ATTENDANCE (5) 50 D
ASSIGNMENTS (10) 35 P
OVER ALL Performance (5) 35 F
References:
A. Beiser, Concept of Modern Physics (or Perspective of Modern Physics),
Tata-McGraw Hill, 2005
Course details
SUB DISCIPLINE: CORE (THEORY)
PH1001: Physics -I (2-1-0)
Relativity: Galilean relativity and Galilean transformation, Special relativity,
Michelson Morley experiment and postulates of relativity, length contraction and time
dilatation, twin paradox, Doppler effect, Lorentz transformation & velocity addition,
relativistic momentum, mass-energy relation, brief introduction to general relativity.
Quantum Mechanics: INADEQUACIES IN CLASSICAL PHYSICS: Black body radiation,
photoelectric effect, X-ray diffraction, Compton Effect, pair production, photon and
gravity, Davisson-Germer experiment WAVE-PARTICLE DUALITY: Particle nature of wave,
Wave nature of particle, de Broglie waves, group waves, phase velocity & group
velocity, uncertainty principle and its application. WAVE FUNCTION: probability & wave
equation, linearity and superposition of wave of wave functions, expectation values
SCHRÖDINGER EQUATION: time dependent and time independent SE, eigenvalue &
eigenfunctions, boundary conditions on wave function, APPLICATION OF SE: Particle in
a box, Finite potential Well, Tunneling through a barrier, Harmonic oscillator.
Essential Readings:
1. A. Beiser, Concept of Modern Physics , Tata-McGraw Hill, 6th edition (2009)
Supplementary Readings:
1. R. Resnick & R. Eisberg, Quantum Physics Of Atoms, Molecules, Solids, Nuclei And
Particles, 2nd Edition.
2. K.S. Krane, Modern Physics, Wiley, 3rd edition (2012).
3. D.J. Griffith, Introduction to Quantum Mechanics, Pearson (2007).
Special Theory of Relativity
Albert Einstein (1879 – 1955) Nobel, 1921 5
5
SPECIAL RELATIVITY
All motion is relative; the speed of light in free space is the same for all
observers
When such quantities as length, time interval, and mass are
considered in elementary physics, no special point is made about how
they are measured.
For instance, there is no question of principle involved in finding the
length of an airplane when we are on board. All we have to do is put
one end of a tape measure at the airplane’s nose and look at the
number on the tape at the airplane’s tail.
But what if the airplane is in flight and we are on the ground? It is not
hard to determine the length of a distant object with a tape measure to
establish a baseline, a surveyor’s transit to measure angles, and a
knowledge of trigonometry.
When we measure the moving airplane from the ground, though, we
find it to be shorter than it is to somebody in the airplane itself. To
understand how this unexpected difference arises we must analyze
the process of measurement when motion is involved. 6
Reference frames
A frame of reference in physics, may refer to a coordinate
system or set of axes within which to measure the
position, orientation, and other properties of objects in it.
y
O x
Inertial frames Non-Inertial frames
z
Accelerating w.r.t. an inertial
No accelerations are observed in the reference frame
absence of external forces Bodies have acceleration in the
Newton’s laws holds good. absence of applied forces
In many cases the earth’s surface can be considered as inertial frame of reference, even
though strictly peaking it is not.
For small scale phenomenon the earth is approximately an inertial frame of reference.
Reference Frames
Platform at rest, tree moving—ball is Platform moving. Observer on
seen by observers on platform as being the ground (inertial frame) sees
deflected, but no force acts on it. ball move in a straight line, but
Violation of Newton’s second law. sees the catcher move away.
Platform is accelerating Ground is the
noninertial frame inertial frame
9
Galilean Transformation
y´
y
S´
v
S
O´ x´
O x
x´ = x – vt
z´ y´ = y
z
z´ = z
Time is absolute t´ = t
Galilean Transformation
y S y´ S´
v EVENT
vt x´
x
x x´
O O´
x´ = x – vt
y´ = y
z´ = z
Time is absolute t´ = t
Historical Perspective
• Light is a wave & waves require a medium through
which to propagate.
• Medium as called the “ether” (from the Greek aither,
meaning upper air).
• Maxwell’s equations assume that light obeys the
Newtonian-Galilean transformation.
• “Water waves travel in water. Sound waves travel in
air. What does light travel in? ether! (Or not.)”
• In the 1880’s Michelson and Morley devised an
experiment to detect the motion of the Earth through
the ether – a universal “atmosphere”.
Concept of Ether &
Michelson-Morley Experiment
• Light should move slower in the direction of the
Earth’s motion through space.
• Experiment designed to measure small changes in
the speed of light was performed by Albert A.
Michelson and Edward W. Morley (1818 – 1905).
• Used an optical instrument called an interferometer
that Michelson invented.
• Device was to detect presence of the ether.
• Outcome of the experiment was negative, thus
contradicting the ether hypothesis.
A.A. Michelson and E.W. Morley, American Journal of Science, 134 – 333, 1887)
Michelson-Morley Experiment
• Albert Michelson (1852–1931) was the first
U.S. citizen to receive the Nobel Prize for
Physics (1907), and built an extremely precise
device called an interferometer to measure
the minute phase difference between two
light waves traveling in mutually orthogonal
directions.
14
Michelson Interferometer
15
Michelson Interferometer
1. AC is parallel to the motion of
the Earth inducing an “ether
wind”
2. Light from source S is split by
mirror A and travels to mirrors C
and D in mutually perpendicular
directions
3. After reflection the beams
recombine at A slightly out of
phase due to the “ether wind” as
viewed by telescope E.
16
Typical interferometer fringe pattern expected
when the system is rotated by 90°
17
The Analysis
Assuming the Galilean Transformation
Time t1 from A to C and back:
Time t2 from A to D and back:
So that the change in time is:
18
The Analysis (continued)
Upon rotating the apparatus, the optical path lengths ℓ1 and
ℓ2 are interchanged producing a different change in time:
(note the change in denominators)
19
Possible Explanations
• Many explanations were proposed but the
most popular was the ether drag hypothesis.
– This hypothesis suggested that the Earth
somehow “dragged” the ether along as it rotates
on its axis and revolves about the sun.
– This was contradicted by stellar abberation
wherein telescopes had to be tilted to observe
starlight due to the Earth’s motion. If ether was
dragged along, this tilting would not exist.
20
Michelson’s Conclusion
Michelson noted that he should be able to detect a phase
shift of light due to the time difference between path
lengths but found none.
He thus concluded that the hypothesis of the stationary
ether must be incorrect.
After several repeats and refinements with assistance
from Edward Morley (1893-1923), again a null result.
Thus, ether does not seem to exist!
Postulates of Special Relativity
The postulates of relativity as stated by Einstein (1905)
1. Equivalence of Physical Laws
The laws of physics are the same in all inertial frames
of reference.
2. Constancy of the Speed of Light
The speed of light in a vacuum, c = 3.00 x 108 m/s, is
the same in all inertial frames of reference,
independent of the motion of the source or the
receiver.
There is no absolute reference frame
of time and space
Albert Einstein (1879–1955) was only two years
old when Michelson reported his first null
measurement for the existence of the ether.
At the age of 16 Einstein began thinking about the
form of Maxwell’s equations in moving inertial
systems.
In 1905, at the age of 26, he published his startling
proposal about the principle of relativity, which
he believed to be fundamental.
