Quantum physics is a branch of science that studies the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. It introduces concepts like wave-particle duality, quantization of energy, and the uncertainty principle, which challenge classical physics.Quantum ph...
Review of classical mechanics (Newtonian mechanics).
Formulated by Sir Isaac Newton (1642-1727 ~ 300 years ago).
Newtons laws
1. Every object must be at rest or moving at a constant speed unless a net
force is acting on it.
2. The rate of change of momentum of an object is equal to the force acting
on it.
3. Every action has an equal and opposite reaction.
Classical mechanics describes the motion of objects based on two
conditions. They are Newton’s second law and the condition that the total
energy of the object is constant (KE + V) = constant.
Force applied to an object = mass of the object acceleration of the object.
F= ma , a = acceleration
Force = rate of change of momentum.
dp
F=
dt
d(mv)
F= m = mass of the object.
dt
m dv d dx m d 2 x
F= = m =
dt dt dt dt 2
1
,At constant acceleration,
dv
m = ma
dt
dv = a dt
v t
dv = a dt
u 0
where, v = final velocity, u = initial velocity
vuv = at t0
v u = at
v = u + at
dx
Using v = dt where x = displacement
∫ ∫ ∫
[ ] [ ] * +
Removing t from the above two equations yields, v 2 = u 2 + 2as
Theorem of equipartition of energy.
For a collection of particles at the temperature T, at thermal equilibrium, the
average contribution to the total energy from each quadratic term is 1/2kT.
Where k = 1.381x10-23 J K-1 (Boltzmann constant).
Eg. Total energy of a particle having three velocity components,
E = ½ mvx2 + ½ mvy2 + ½ mvz2
2
, = ½ kT + ½ kT + ½ kT
= 3/2 kT
Eg. Energy of a particle attached by a spring (force constant k) and free to
move in 1-D,
E = ½ mvx2 + ½ kx2
= kT
Newtonian mechanics is successful in describing motion of large objects.
Evidence began to appear after 1900 that Newtonian mechanics is
unsuccessful in describing the motion of elementary particles (electrons,
protons etc.), atoms and molecules.
Paradoxes in classical physics
Black body radiation
(quantization of energy)
The intensity and wavelength of electromagnetic radiation emitted by a
black body depends on temperature. A black body can absorb all the
wavelengths of electromagnetic radiation falling on it. The closest example
for a black body is a pinhole on a hollow dark sphere. Classical prediction of
8kT
the intensity of emitted radiation is given by, (Rayleigh-Jeans law).
λ4
= energy emitted per unit volume per unit wavelength, k = Boltzmann
constant, T = temperature, = wavelength of emitted radiation. According
3
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