文档介绍：Applied Quantum Mechanics
Chapter 1 Problems and Solutions
LAST NAME FIRST NAME
Useful constants MKS (SI)
Speed of light in free space c = ´ 108 m s–1
–16
Planck’s constant h = ()6 ´ 10 eV s
–34
h = ()2 ´ 10 J s
Electron charge e = ()3 ´ 10–19C
–31
Electron mass m0 = ()2 ´ 10 kg
–27
Neutron mass mn = ()3 ´ 10 kg
–27
Proton mass mp = ()3 ´ 10 kg
–23 –1
Boltzmann constant kB = ()4 ´ 10 J K
–5 –1
kB = ()5 ´ 10 eV K
–12 –1
Permittivity of free space e0 = ´ 10 F m
–7 –1
Permeability of free space m0 = 4p ´ 10 H m
Speed of light in free space c = 1 ¤ e0m0
23 –1
Avagadro’s number NA = ()9 ´ 10 mol
–10
Bohr radius aB = ()9 ´10 m
2
4pe0h
aB = ----------------2 -
m0e
Inverse fine-structure constant a–1 = ( 0)
4pe c
a–1 = -----------------0h -
e2
Applied quantum mechanics 1
PROBLEM 1
A metal ball is buried in an ice cube that is in a bucket of water.
(a) If the ice cube with the metal ball is initially under water, what happens to the water level
when the ice melts?
(b) If the ice cube with the metal ball is initially floating in the water, what happens to the water
level when the ice melts?
(c) Explain how the Earth’s average sea level could have increased by at least 100 pared
to about 20,000 years ago.
(d) Estimate the thickness and weight per unit area of the ice that melted in (c). You may wish
to use the fact that the density of ice is 920 kg m-3, today the land surface area of the Earth is about
148,300,000 km2 and water area is about 361,800,000 km2.
PROBLEM 2
Sketch and find the volume of the largest and smallest convex plug manufactured from a sphere
of radius r = 1 cm to fit exactly into a circular hole of radius r = 1 cm, an isosceles triangle with
base 2 cm and a height h = 1 cm, and a half circle radius r = 1 cm and base 2 cm.
PROBLEM