Classical mechanics describes macroscopic objects while quantum mechanics describes microscopic objects due to limitations of classical theory. Quantum mechanics was introduced after classical mechanics failed to explain experimental observations involving microscopic particles. Some key aspects of quantum mechanics are the photoelectric effect, blackbody radiation, Compton effect, wave-particle duality, the Heisenberg uncertainty principle, and Schrodinger's wave equation. Schrodinger's equation describes the wave function and probability of finding a particle.

1. Introduction to Quantum Mechanics
and Schrodinger Equation
 SUBMITTED BY :- 1. GAURAV
SINGH
2.DEEPAK MEENA
 CLASS :- B.Sc.(H)
CHEMISTRY
 SEMESTER :- Vth SEMESTER
 ROLL NO. :-
18/76022(GAURAV)

2. Classical Mechanics and Quantum
Mechanics
Mechanics: the behavior study of matter
when it is in motion is called as Mechanics.
Classical Mechanics: describing
the motion of macroscopic objects.
Macroscopic: measurable or
observable by naked eyes
Quantum Mechanics: describing
behavior of systems at atomic
length scales and smaller i.e.
microscopic objects.

3. Introduction to Quantum
Mechanics
Ques.:- Why Quantum Mechanics is introduced?
OR
Necessity of Quantum Mechanics?
Ans. :- Quantum Mechanics is introduced after the
failure of Classical mechanics. Earlier it was
thought that the laws of classical mechanics
could explain the motion of both macroscopic and
microscopic particles. But later on experimental
studies showed that classical mechanics failed
when applied to microscopic objects such as
electron, proton, etc.

4. Limitations of Classical Theory of
radiation
 Classical Theory of radiation was not able to
explain the following observations:-
1. Black body radiation
2. Photoelectric effect
3. Compton effect
4. Variation of heat capacity of solids as a function
of temperature.
5. Line spectra of atoms with special reference to
hydrogen.

5. Photo Electric Effect
 The emission of electrons from a metal plate
when illuminated by light or any radiation of
suitable wavelength or frequency is called Photo
electrons.

6. 6
6
Photoelectric Effect
T
max
0
ν
νo
• Inconsistency with classical light theory
According to the classical wave theory, maximum kinetic energy of the photoelectron
is only dependent on the incident intensity of the light, and independent on the light
frequency; however, experimental results show that the kinetic energy of the
photoelectron is dependent on the light frequency.
Metal Plate
Incident light with
frequency ν
Emitted electron
kinetic energy = T
The photoelectric effect ( year1887 by Hertz) Experiment results
Concept of “energy quanta”

7. Black-Body Radiation
 A black body is an ideal body which allows the
whole of the incident radiation to pass into
itself (without reflecting the energy) and
absorbs within itself this whole incident radiation
(without passing on the energy). This property is
valid for radiation corresponding to all wavelengths
and to all angels of incidence. Therefore, the black
body is an ideal absorber of incident radiation.

8. Compton Effect
 When a monochromatic beam of X-rays is
scattered from a material then both the
wavelength of primary radiation (unmodified
radiation ) and the radiation of higher wavelength
(modified radiation) are found to be present in the
scattered radiation. Presence of modified
radiation in scattered X-rays is called Compton
effect.

9. Max Planck
 In 1900, Max Planck initiated
Quantum Physics by presenting
his Quantum Theory.
 He was awarded Nobel Prize
in Physics in 1918.

10. Planck’s Quantum Theory
 Main Points of this Theory are:
a. Energy is not emitted or absorbed continuously. It is emitted or
absorbed in the form of wave packets or quanta.
In case of light, the quantum of energy is often called Photon.
b. The amount of energy associated with quantum of radiation is
directly proportional to the frequency of radiation.
c. A body can emit or absorb energy only in terms of integral multiple
of a quantum/ photon.
where n =1,2,3,….

nh
E 


h
E
E



11. Ques.:- Why Classical Mechanics failed for
microscopic objects?
Ans.:- This is mainly because Classical Mechanics did
not take into account the concept of de-Broglie Dual
nature of matter and Heisenberg’s Uncertainty
Principle. Also, it does not put any restriction on the
values of dynamical properties (such as position,
magnitude, etc) calculated for microscopic objects
and hence Classical Mechanics was failed.
Therefore, to understand the behavior of such
objects, Quantum Mechanics was introduced.

12. Wave-Particle Duality
Particle-like wave behavior
(example, photoelectric effect)
Wave-like particle behavior
(example, Davisson-Germer experiment)
Wave-particle duality
Mathematical descriptions:
The momentum of a photon is:

h
p 
The wavelength of a particle is:
p
h


λ is called the de Broglie wavelength

13.  Proposed by French physicist, Louis-Victor de-
Broglie.
 He suggested that, just as radiation possesses
dual behavior i.e. Wave nature as well as particle
nature, all microscopic and macroscopic materials
also possess dual nature (i.e. wave and particle
nature).
 De Broglie, gave the following relation between
wavelength (λ) and momentum (p) of a material
particle.
λ= h/mv = h/p
[here λ is
wavelength, p is the momentum and h is
de-Broglie Dual nature of
matter

14. The Uncertainty Principle
The Heisenberg Uncertainty Principle (year 1927):
• It is impossible to simultaneously describe with absolute accuracy the
position and momentum of a moving microscopic particle.
• It is impossible to simultaneously describe with absolute accuracy the
energy of a particle and the instant of time the particle has this energy

4
/
h
x
p 



4
/
h
t
E 


The Heisenberg uncertainty principle applies to electrons and states
that we can not determine the exact position of an electron. Instead, we
could determine the probability of finding an electron at a particular
position.

15. Schrӧdinger’s Wave Equation
 Schrödinger equation is the
fundamental equation of the science of
submicroscopic phenomena known as Quantum
Mechanics.
 The equation, developed (1926)
by the Austrian physicist
Ervin Schrodinger, has the same
central importance to Quantum
Mechanics as Newton’s laws of
motion have for the large-scale
phenomena of classical mechanics.

16.  The Schrödinger equation is a linear partial differential
equation that describes the wave function or state function of a
quantum-mechanical system.
 Essentially a wave equation, the Schrödinger equation describes the
form of the probability waves (or wave functions ) that govern the
motion of small particles.
 It specifies how these waves are altered by external influences.
Schrödinger established the correctness of the equation by applying
it to the hydrogen atom, predicting many of its properties with
remarkable accuracy. The equation is used extensively in atomic,
nuclear, and solid-state physics.

17. Schrodinger’s Equation
Time Independent Schrodinger’s
Equation
Time dependent Schrodinger’s
Equation
If the particle is moving in 3-
dimensional space then,

18. Erwin Rudolf Josef Alexander Schrödinger
Austrian
1887 –1961
Without potential E = T
With potential E = T + V
Time-dependent Schrödinger Equation

19.  The equation takes into account the dual nature of matter and is
given as:-
 The solution of Schrodinger wave equation for an electron give the
values of E and Ψ.
 The values of E represent the possible values of energy which the
electron in the atom can occupy. The corresponding values of Ψ are
called wavefunctions. The wavefunction corresponding to an
energy state contains all the information about an electron which is
present in that state.

20. Wave function
The quantity with which Quantum Mechanics is
concerned is the wave function of a body.
Wave function, Ψ is a quantity associated with a moving
particle. It is a complex quantity.
|Ψ|2 is proportional to the probability of finding a
particle at a particular point at a particular time. It is
the probability density.
|Ψ|2 = Ψ*Ψ
Thus if Ψ = A+ iB then Ψ* = A− iB
⇒|Ψ |2 = Ψ*Ψ = A2 − i2 B2 = A2 + B2

21. Properties of wave function
1. It must be finite everywhere.
If ψ is infinite for a particular point, it mean an
infinite large probability of finding the particles at
that point. This would violates the uncertainty
principle.
2. It must be single valued.
If ψ has more than one value at any point, it
mean more than one value of probability of finding
the particle at that point which is obviously wrong.
3. It must be continuous and have a continuous first
derivative everywhere.
4. It must be normalisable.
5.It must be bounded in the space.