De Broglie's postulate - wave-like properties of particles
Wave-particle duality
Electromagnetic radiation can exhibit both particle and wave properties. It appears dicult to reconcile
these facts.
Th
Models of an atom and old quantum theory
Classical models of atoms
Thompson's model
Chemical elements dier by the number Z of electrons in their atoms. Atoms are electrically neutral,
so that the cha
Mid-term Exam Solutions
1. (a) The explorer travels in two stages, the trip to the star and the trip back home. Each trip lasts
t = 40 years as observed on earth, but it corresponds to a shorter time
Homework 3: Quantization of electromagnetic radiation
1. A typical chemical bond in a biological molecule has a strength of a few electron-volts, say 4 eV to be
specic.
(a) Can low-intensity microwave
Homework 6: Schrodinger equation
1. Important properties of complex numbers:
(a) Use Euler's formula ei = cos + i sin to express a complex number z = x + iy as z = rei . Write
x and y in terms of r an
Homework 4: Matter waves
1. Consider a head-on elastic collision between a photon of momentum p0 and a stationary free electron.
(a) Calculate the momentum p of the photon after collision assuming tha
Special theory of relativity
Electrodynamics and Michelson-Morley experiment
At the end of the 19th century physics was solidly shaped by two great theories: Newton's mechanics
and Maxwell's electrody
Relativistic dynamics
Lorentz transformations also aect the accelerated motion of objects under the inuence of forces. In
Newtonian physics a constant force
that the velocity
v = at
F
accelerates an a
Solutions to homework 4: Matter waves
1. (a) The incoming photon with momentum
pe
p0 kicks the electron and bounces back, giving a momentum
p0 . Projecting all momenta onto the positive x axis, the
to
Solutions to homework 3: Quantization of electromagnetic radiation
1. (a) No. Energy of a photon with = 1 cm is 0.12 meV, which is not enough to break a bond.
(b) hc/ > Ebond < hc/Ebond = 310 nm
(c) T
Solutions to homework 5: Atomic spectra
1. The Rydberg formula for the Hydrogen atom emission spectrum is
1
=R
1
1
2
m2
n
,
n>m1
Each series of emission wavelengths, obtained by xing m and varying n,
z = rei = r(cos + i sin ) = x + iy
x = r cos y = r sin
x2 + y 2 = r2 (cos2 + sin2 ) = r2 r = x2 + y 2 y/x = tan
= arctan(y/x) f (z) = arctan(z)
2
z (/2, /2)
arctan 2
x y
(, )
2m = 2
E = 2mc2 M
h
E = M gh g 9.8 2
M=
2mc2
1.83 1010
gh
E = mc2 E0 = mc2
E
1
=
2
E0
1 (v/c)
=
v2
=
c2
1
v=c
t=
l
=
v
2
E0
E
E0
E
1
2
l
l
c
1
E0 2
E
tl
=
E0 2
E
1
l = ctl t
Schrodinger equation in three dimensions
The stationary Schrodinger equation in three dimensions is a partial dierential equation involving three
coordinates per particle.
The mathematical complexity
Quantum Mechanics
Dynamics of matter waves
We learned that the discoveries such as blackbody radiation and photoelectric eect led to a general
conclusion that energy of electromagnetic waves is transf