Quantum Mechanics

APPLIED
PHYSICS
1
CODE : 07A1BS05
I B.TECH
CSE, IT, ECE & EEE
UNIT-2
NO. OF SLIDES : 18
UNIT INDEX
UNIT-2
S.No
.
Module
Lectur PPT Slide

e
No.
No.
1
2
Waves & Particles Plancks Quantum

theory.
De Broglie
hypothesis, matter
L1
L2
6-9
L3-4
10
waves.
Verification of matter
waves
Schrdingers
time independent
wave equation
6
Physical
significance of
wave function
Particle in one
dimensional
potential box.
L6
13-14
L7
15-16
L8
17-18
Introduction
Lecture-1
1. According to Planks quantum theory,

energy is emitted in the form of packets
or quanta called Photons.
2. According to Planks law, the energy of
photons per unit volume in black body
radiation is given by
E=85[exp(h/kT) -1]
5
Waves-particles
2
Lecture-
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 =h/m
and is called de Broglie wavelength
6
Characteristics of matter waves

Lecture-3
Since =h/m,
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, =. 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
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. Heisenbergs uncertainty principle is
based on this concept.
8
Difference between matter wave

and E.M.wave::
Matter waves
1.Matter wave is associated
with moving particle.
2Wavelength depends on the
mass of the particle and its
velocity =h/m
3. Can travel with a velocity
greater than the velocity of
light.
4.Matter wave is not
electromagnetic wave.
E.M.wave
1.Oscillating charged particle
give rise to e.m. wave.
2.Wave length depends on the
energy of photon
=hc/E
3. Travel with velocity of light
c=3x108 m/s
4.Electric field and magnetic
field oscillate perpendicular to
each other.
9
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
Heisenbergs 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.
xp h/4
11
9.If E and t are the uncertainties in the

measurements of energy and time of a
system, according to uncertainty
parinciple.
Et h/4
12
Schrdinger 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
The one dimensional time

independent schrodinger wave
equation is given by
d2/dx2 +
[2m(E-V)/ 2] =0
(or)
d2/dx2+ [82m(E-V) / h2] =0
14
Physical significance of Wave

function
Lecture-7
1. The wave functions n 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 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
3.* or ||2 is the probability density
function. *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
*dxdydz=1
4.It can be considered as probability

amplitude since it is used to find the
location of the particle.
16
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 Schrdinger
wave equation and simplifying we get

the energy of the nth quantum level,
17
En=(n222)/2mL2= n2h2/8mL2
When the particle is in a potential
well of width L, n=(2/L)sin(n/L)x
& En = n2h2/8mL2,n=1,2,3,.
When the particle is in a potential
box of sides Lx,Ly,Lz n=(8/V)sin(nx
/Lx) x sin (ny /Ly) ysin (nz /Lz)z.
Where nx, ny or nz is an integer under
the constraint n2= nx2+ny2+ nz 2.
18

Quantum Mechanics

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APPLIED

Lectur PPT Slide

Waves & Particles Plancks Quantum

1. According to Planks quantum theory,

According to Louis de Broglie since

Characteristics of matter waves

6.No single phenomena exhibits both particle nature

Difference between matter wave

Davisson and Germer provided

Heisenbergs uncertainty principle

It is impossible to specify precisely and

9.If E and t are the uncertainties in the

Schrdinger wave equation

Schrodinger developed a differential

The one dimensional time

Physical significance of Wave

1. The wave functions n and the corresponding

energies En, which are often called eigen functions

2.The wave function has no direct physical

3.* or ||2 is the probability density

function. *dxdydz gives the probability

4.It can be considered as probability

Particle in one dimensional

Quantum mechanics has many

wave equation and simplifying we get

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