2. CODE : 07A1BS05
I B.TECH
CSE, IT, ECE & EEE
UNIT-2
NO. OF SLIDES : 18
2
3. UNIT INDEX
UNIT-2
S.No Module Lectur PPT Slide
. e No.
No.
1 Waves & Particles - L1 5
Planck’s Quantum
theory.
2 De Broglie L2 6-9
hypothesis, matter
waves.
3 Verification of matter L3-4 10
waves
4 Heisenberg uncertainty L5 311-12
principle.
4. 5 Schrödinger’s L6 13-14
time independent
wave equation
6 Physical L7 15-16
significance of
wave function
7 Particle in one L8 17-18
dimensional
potential box.
4
5. Introduction Lecture-1
1. According to Plank’s quantum
theory, energy is emitted in the form
of packets or quanta called Photons.
2. According to Plank’s law, the energy
of photons per unit volume in black
body radiation is given by
Eλ=8πһс∕λ5[exp(h/טkT) -1]
5
6. Waves-particles
Lecture-
2
According to Louis de Broglie since
radiation such as light exhibits dual nature
both wave and particle, the matter must
also posses dual nature.
The wave associated with matter called
matter wave has the wavelength λ=h/mט
and is called de Broglie wavelength
6
7. Characteristics of matter waves
Lecture-3
Since λ=h/m,ט
1. Lighter the particle, greater is the wavelength
associated with it.
2. Lesser the velocity of the particle, longer the
wavelength associated with it.
3. For v=0, λ=∞. This means that only with
moving particle matter wave is associated.
4. Whether the particle is charged or not, matter
wave is associated with it. This reveals that these
waves are not electromagnetic but a new kind of
waves. 7
8. 6.No single phenomena exhibits both particle nature
and wave nature simultaneously.
7. While position of a particle is confined to a
particular location at any time, the matter wave
associated with it has some spread as it is a wave.
Thus the wave nature of matter introduces an
uncertainty in the location of the position of the
particle. Heisenberg’s uncertainty principle is
based on this concept.
8
9. Difference between matter
wave and E.M.wave::
Matter waves E.M.wave
1.Matter wave is associated 1.Oscillating charged particle
with moving particle. give rise to e.m. wave.
2Wavelength depends on the 2.Wave length depends on the
mass of the particle and its energy of photon
velocity λ=h/mט λ=hc/E
3. Can travel with a velocity 3. Travel with velocity of light
greater than the velocity of c=3x108 m/s
light. 4.Electric field and magnetic
4.Matter wave is not field oscillate perpendicular to
electromagnetic wave. each other.
9
10. Lecture-4
Davisson and Germer provided
experimental evidence on matter wave
when they conducted electron diffraction
experiments.
G.P.Thomson independently conducted
experiments on diffraction of electrons
when they fall on thin metallic films.
x
10
11. Heisenberg’s uncertainty principle
Lecture-5
“It is impossible to specify precisely and
simultaneously the values of both
members of particular pair of physical
variables that describe the behavior an
atomic system”.
If ∆x and ∆p are the uncertainties in the
measurements of position and momentum
of a system, according to uncertainty
principle.
∆x∆p≥ h/4π
•
11
12. 9.If ∆E and ∆t are the uncertainties in the
measurements of energy and time of a
system, according to uncertainty
parinciple.
∆E∆t≥ h/4π
12
13. Schrödinger wave equation Lecture-6
Schrodinger developed a
differential equation whose solutions
yield the possible wave functions
that can be associated with a
particle in a given situation.
This equation is popularly known as
schrodinger equation.
The equation tells us how the wave
function changes as a result of
forces acting on the particle.
13
14. • The one dimensional time
independent schrodinger wave
equation is given by d2Ψ/dx2 +
[2m(E-V)/ ћ2] Ψ=0
(or)
d2Ψ/dx2+ [8π2m(E-V) / h2] Ψ=0
14
15. Physical significance of Wave
function Ψ Lecture-7
1. The wave functions Ψn and the corresponding
energies En, which are often called eigen functions
and eigen values respectively, describe the
quantum state of the particle.
2.The wave function Ψ has no direct physical
meaning. It is a complex quantity
representing the variation of matter wave.
It connects the particle nature and its
associated wave nature.
15
16. 3.ΨΨ* or |Ψ|2 is the probability density
function. ΨΨ*dxdydz gives the probability
of finding the electron in the region of
space between x and x+dx, y and y+dy and
z and z+dz.If the particle is present∫
∫ΨΨ*dxdydz=1
4.It can be considered as probability
amplitude since it is used to find the
location of the particle.
16
17. Particle in one dimensional
potential box Lecture-8
• Quantum mechanics has many
applications in atomic physics.
• Consider one dimensional potential well
of width L.
• Let the potential V=0inside the well and
V= ∞outside the well.
• Substituting these values in Schrödinger
wave equation and simplifying we get
the energy of the nth quantum level,
17
18. • En=(n2π2ћ2)/2mL2= n2h2/8mL2
• When the particle is in a potential
well of width L, Ψn=(√2/L)sin(nπ/L)x
& En = n2h2/8mL2,n=1,2,3,….
• When the particle is in a potential
box of sides Lx,Ly,Lz Ψn=(√8/V)sin(nx
π/Lx) x sin (ny π/Ly) ysin (nz π/Lz)z.
• Where nx, ny or nz is an integer under
the constraint n2= nx2+ny2+ nz 2. 18
