Quantum mechanics

Quantum Mechanics Chapter Two Dr Azeez Barzinjy
42
Classical interpretation: interference pattern appears due to interference
between waves passing through the two different slits.
Quantum view: a photon might be described as wavelike while passing
in the slits but becomes particle when it interacts with the
screen (duality)
Problem Set (2)
Q1 (a) does the de Broglie wavelength apply only to “elementary
particles” such as an electron or neutron or does it apply as well to
compound systems of matter having internal structure? Give examples.
(b) If in the de Broglie formula, we will let m→∞, do we get classical
result for microscopic particles?
Q2 Discuss similarities and differences between a matter wave and an
electromagnetic wave.
Q3 Show that for a free particle the uncertainty relation can also be written
as ∆λ∆x ≥
λ
2

where ∆x is the uncertainty in location of the wave and ∆λ
the simultaneous uncertainty in wavelength.
Q4 If ∆λ
λ
= 10−7
for a photon, what is the simultaneous value of ∆x for:
(a) λ = 5 × 10−4A
o
(𝑋 − ray)?
(b) λ = 5 A
o
(𝑋 − ray)?
(c) λ = 5000 A
o
(yellow light)?
Screen
Light
waves
Interference pattern demonstrates wave properties.
Quantum Mechanics Chapter Two Dr Azeez Barzinjy
43
Q5 A microscope using photon is employed to locate an electron in an
atom to within a distance of 0.2 A
o
.What is the uncertainty in the velocity
of the electron located in this way?
Q6 A laser beam λ = 632.8 nm is incident on two slits 0.2mm apart. How
far apart are the bright interference fringes on screen 5m away from the
double-slits?
Q7 You can read these words because particles of light, photons, have
bounced off the screen or paper and reached your eyes. Why you cannot
do so, similarly, bounce a photon off an electron and detect that photon
with an instrument?
Q8 Discuss how Heisenberg’s uncertainty principle can explain a type of
nuclear radiation called alpha decay?
Note: Alpha particles are two protons and two neutrons emitted by some
heavy nuclei, such as uranium 238.
Q9 A localized particle in Quantum Mechanics is described by a wave
packet in position space, regardless of its energy. However, from the point
of view of General Relativity, if the particle’s energy density exceeds a
certain threshold, it should be a black hole. Explain this statement
carefully.
Practice Tests
P1 An attempt carefully observes the electron orbit leads to an
uncontrollable perturbation of the observe system.
Sol. 1:
𝜆 << 𝑎 observed from x-ray
a: is a radius of 1st Bohr orbit ~53 pm
For electron ∆p ~

λ

λ


a
,

a
=
6.62 × 10−34
2π(53 × 10−12)
≈ 2 × 10−24kg.
m
s
𝜆
a

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