4: Wave mechanical concepts

Example number 4.1, Page number 59

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;    #planck's constant(Js)
e=1.6*10**-19;   #conversion factor from J to eV
m=9.1*10**-31;    #mass of electron(kg)
V=1;    #assume

#Calculation
lamda=h/math.sqrt(2*m*e*V);    #debroglie wavelength(m)

#Result
print "debroglie wavelength is math.sqrt(",int((lamda*10**10)**2),"/V) angstrom"

debroglie wavelength is math.sqrt( 150 /V) angstrom

Example number 4.2, Page number 59

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;    #planck's constant(Js)
c=3*10**8;    #velocity of light(m/sec)
e=1.6*10**-19;   #conversion factor from J to eV
m=9.1*10**-31;    #mass of electron(kg)
KE=100*10**6;   #kinetic energy(eV)

#Calculation
p=math.sqrt(2*m*e);     #momentum(kg m/s)
lamda1=h/p;    #debroglie wavelength for 1 eV(m)
lamda2=h*c/(KE*e);    #debroglie wavelength for 100 MeV(m)

#Result
print "debroglie wavelength for 1 eV is",round(lamda1*10**9,1),"nm"
print "debroglie wavelength for 100 MeV is",round(lamda2*10**15,2),"*10**-15 m"

debroglie wavelength for 1 eV is 1.2 nm
debroglie wavelength for 100 MeV is 12.42 *10**-15 m

Example number 4.3, Page number 64

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=9.1*10**-31;    #mass of electron(kg)
v=4*10**6;    #speed of electron(m/s)
sp=1/100;     #speed precision
hbar=1.05*10**-34;  

#Calculation
p=m*v;   #momentum(kg m/s)
deltap=p*sp;    #uncertainity in momentum(kg m/s)
deltax=hbar/(2*deltap);   #precision in position(m)

#Result
print "precision in position is",round(deltax*10**9,2),"nm"

precision in position is 1.44 nm

Example number 4.4, Page number 64

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
lamda=4000*10**-10;    #wavelength(m)
deltat=10**-8;    #average lifetime(s)

#Calculation
delta_lamda=lamda**2/(4*math.pi*c*deltat);   #width of line(m)

#Result
print "width of line is",round(delta_lamda*10**15,2),"*10**-15 m"

width of line is 4.24 *10**-15 m