MA 1505 Mathematics I
Tutorial 11 Solutions
1. We have
f (r(u, v ) = f (2u + v, u 2v, u + 3v ) = 2u + v + u 2v + u + 3v = 4u + 2v,
F(r(u, v ) = F(2u + v, u 2v, u + 3v ) = (2u + v )2 i + (u 2v )2 j + (u + 3v )2 k,
ru rv = (2i + j + k) (i 2j + 3k) = 5i 5j 5
GEK1508/PC1325
Einsteins Universe and
Quantum Weirdness
Tutorial 5
1. Why classify fundamental fermions into quarks and
leptons?
2. Helium nucleus is made up of fermions (2 protons, 2
neutrons). Why it is a boson?
3. What are anti-particles?
4. Can spin o
GEK1508/PC1325
Einsteins Universe and
Quantum Weirdness
Tutorial 4
1. Do neutrons behave the same way as electrons in the
double slit experiment?
2. What is the value for xpy?
3. Is the uncertainty relation x(t1)px(t2) zero for t1 t2?
4. What are the prob
GEK1508/PC1325
Einsteins Universe and
Quantum Weirdness
Tutorial 3
Classical Quantum
b
a
c
1. Qualitative description of Einsteins
field equation
2. Roles of the metric
3. What is vacuum fluctuation?
c 2 a 2 b 2 2ab cos
(1) From the discussion given in th
GEK1508/PC1325
Einsteins Universe and
Quantum Weirdness
Tutorial 2
What is the purpose of the irritating negative sign in the
Minkowskis metric?
Is spacetime interval an invariant quantity?
Is the energy dispersion relation an invariant quantity?
What
GEK1508/PC1325
Einsteins Universe and
Quantum Weirdness
Tutorial 1
What is the speed of light measured by a
massless person moving at speed of light?
Is simultaneous events relative?
Can we communicate with someone outside
our lightcone?
Can you appre