[MATLAB图书合集].Applied-Quantum-Mechanics-2nd-Ed.Solutions.Manual.

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Applied quantum mechanics 1

Applied Quantum Mechanics

Chapter 1 Problems and Solutions

LAST NAME FIRST NAME

Useful constants MKS (SI)

Speed of light in free space

Planck’s constant

Electron charge

Electron mass

Neutron mass

Proton mass

Boltzmann constant

Permittivity of free space

Permeability of free space

Speed of light in free space

Avagadro’s number

Bohr radius

Inverse fine-structure constant

c 2.9979245810

× m s

–

6.5821188926()10

–

× eV s=

1.05457159682()10

–

× J s=

e 1.60217646263()10

–

× C=

9.1093818872()10

–

× kg=

1.6749271613()10

–

× kg=

1.6726215813()10

–

× kg=

1.380650324()10

–

× J K

–

8.61734215()10

–

× eV K

–

8.854187810

–

× F m

–

4π 10

–

× H m

–

c 1 ε

⁄=

6.0221419979()10

× mol

–

0.5291772119()

–

×10 m=

4πε

-----------------=

–

137.03599765

(

)

1–

πε

------------------=

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?

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 km

and water area is about 361,800,000 km

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 3

An initially stationary particle mass m

is on a frictionless table surface and another particle

mass m

is positioned vertically below the edge of the table. The distance from the particle mass

to the edge of the table is l. The two particles are connected by a taught, light, inextensible

string of length L > l.

(a) How much time elapses before the particle mass m

is launched off the edge of the table?

(b) What is the subsequent motion of the particles?

PROBLEM 4

The velocity of water waves in shallow water may be approximated as where g is the

acceleration due to gravity and h is the depth of the water. Sketch the lowest frequency standing

water wave in a 5 m long garden pond that is 0.9 m deep and estimate its frequency.

PROBLEM 5

(a) What is the dispersion relation of a wave whose group velocity is half the phase velocity?

(b) What is the dispersion relation of a wave whose group velocity is twice the phase velocity?

PROBLEM 6

A stationary ground-based radar uses a continuous electromagnetic wave at 10 GHz frequency

to measure the speed of a passing airplane moving at a constant altitude and in a straight line at

1000 km hr

-1

. What is the maximum beat frequency between the out going and reflected radar

beams? Sketch how the beat frequency varies as a function of time. What happens to the beat fre-

quency if the airplane moves in an arc?

vgh=

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