Download Quantum Mechanics: Introduction

Birthday
of
Quantum Physics
on
14th December, 1900
E  h
Planck introduces a new
fundamental constant
Max Karl Ernst Ludwig Planck
1858-1947
h
to explain black-body radiation
Blackbody Radiation
~
Energy density
in the window
υ and υ +d υ
ρ(υ)
3
J/m -Hz
hυ = kT
h :Planck’s constant
= 6.63 x 10
-34
J-s
k=:Boltzmann’s const.
= 1.38 x 10
= R/N
-23
T=1800 K
T=1400 K
T=1000 K
frequency υ
J/K
Classical concept
Two distinct categories :
1. Material body (particle)
Newton’s laws of motion
Position and velocity (momentum) are
precisely measurable
Spread over the space, amplitude gives
2. Electromagnetic field (wave)
energy/intensity, frequency is nothing
Maxwell’s equation
but time periodicity of oscillator
Additionally
Laws of thermodynamics
E = kT
Fundamental constants :
1. velocity of light c
2. Avogadro Number N
3. Boltzman constant k
4. Unit of charge e
E = mc2
Velocity << c : non-relativistic
Velocity comparable to c : relativistic
Classical concepts never allow to think that
1. Wave may also behave like particle.
(Planck’s hypothesis)
2. Particle may behave like wave.
(de Broglie hypothesis)
3. Position and momentum of a particle cannot
be measured accurately simultaneously.
(Heisenberg uncertainty principle)
4. Energy of wave is related with frequency
and quantised.
E  nh
These new concepts is basically quantum concepts
Rayleigh-Jeans law
Classical theory
T=1800 K
ρ(υ)
T=1800 K
T=1400 K
T=1000 K
frequency υ
ρ(υ)
T=1800 K
υ dependence
2
frequency υ
Planck’s Formula
Rayleigh-Jeans law
Planck’s postulate
Any physical entity with one degree of freedom
and whose ``co-ordinate” is oscillating
sinusoidally with frequency
can possess only
total energies E as integral multiple of
h = Planck’s constant
4
Classical
2
E=0
particle wave duality
de Broglie postulate
waves behaving as particles
Experiments
1. Photoelectric effect (1902)
2. Compton effect (1922)
3. Pair Production
particles behaving as waves
Experiments
1. Electron diffraction
Davisson –Germer (USA)
and Thompson (UK) (1927)
2. Electron microscope