6: Principles of Quantum Mechanics

Example number 1, Page number 6.22

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=344;         #voltage(V)
theta=40;      #angle(degrees)
n=1; 

#Calculation
lamda=12.26/math.sqrt(V);    #deBroglie wavelength(angstrom)
theta=((180-theta)/2)*math.pi/180;    #angle(radian)
d=n*lamda/(2*math.sin(theta));        #spacing between planes(angstrom)

#Result
print "deBroglie wavelength is",round(lamda,2),"angstrom"
print "spacing between planes is",round(d,2),"angstrom"

deBroglie wavelength is 0.66 angstrom
spacing between planes is 0.35 angstrom

Example number 2, Page number 6.22

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;       #charge(coulomb)
m=1.675*10**-27;     #mass(kg)
E=10*10**3*e;        #kinetic energy(J)
h=6.625*10**-34;     #planks constant(Js)

#Calculation
v=math.sqrt(2*E/m);    #velocity(m/sec)
lamda=h*10**10/(m*v);  #deBroglie wavelength(angstrom)

#Result
print "deBroglie wavelength is",round(lamda,5),"angstrom"

deBroglie wavelength is 0.00286 angstrom

Example number 3, Page number 6.22

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=9.1*10**-31;     #mass(kg)
h=6.63*10**-34;    #planks constant(Js)
a=1;               #length(m)
nx1=1;
ny1=1;
nz1=1;
nx2=1;
ny2=1;
nz2=2;

#Calculation
E1=h**2*(nx1**2+ny1**2+nz1**2)/(8*m*a**2);     #energy of 1st quantum state(J)
E2=h**2*(nx2**2+ny2**2+nz2**2)/(8*m*a**2);     #energy of 2nd quantum state(J)
E=E2-E1;          #energy difference(J)

#Result
print "energy difference is",round(E*10**37,2),"*10**-37 J"

energy difference is 1.81 *10**-37 J

Example number 4, Page number 6.23

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

#Variable declaration
m1=9.1*10**-31;     #mass(kg)
m2=0.05;            #mass(kg)
v=300;              #velocity(m/sec)
p=0.01/100;         #probability
h=6.6*10**-34;      #planks constant(Js)

#Calculation
p1=m1*v;            #momentum of electron(kg m/s)
deltap1=p*p1;      
deltax1=h/(deltap1*4*math.pi);   #uncertainity in position of electron(m)
p2=m2*v;            #momentum of bullet(kg m/s)
deltap2=p*p2;      
deltax2=h/(deltap2*4*math.pi);   #uncertainity in position of bullet(m)

#Result
print "uncertainity in position of electron is",round(deltax1,3),"m"
print "uncertainity in position of bullet is",round(deltax2*10**31,1),"*10**-31 m"

uncertainity in position of electron is 0.002 m
uncertainity in position of bullet is 0.4 *10**-31 m

Example number 5, Page number 6.24

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
deltax=10**-10;     #uncertainity in position(m)
L=10*10**-10;       #width(m)

#Calculation
p=2*deltax/L;       #probability of finding the particle

#Result
print "probability of finding the particle is",p

probability of finding the particle is 0.2

Example number 6, Page number 6.24

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;       #charge(coulomb)
m=9.1*10**-31;       #mass(kg)
E=2*10**3*e;         #kinetic energy(J)
h=6.6*10**-34;       #planks constant(Js)

#Calculation
p=math.sqrt(2*E*m);    #momentum(kg m/s)
lamda=h/p;             #deBroglie wavelength(m)

#Result
print "deBroglie wavelength is",round(lamda*10**11,2),"*10**-11 m"

deBroglie wavelength is 2.73 *10**-11 m

Example number 7, Page number 6.24

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.602*10**-19;       #charge(coulomb)
m=1.676*10**-27;       #mass(kg)
h=6.62*10**-34;        #planks constant(Js)
E=0.025*e;             #kinetic energy(J)

#Calculation
mv=math.sqrt(2*E*m);    #velocity(m/s)
lamda=h*10**10/mv;      #deBroglie wavelength(angstrom)

#Result
print "deBroglie wavelength is",round(lamda,3),"angstrom"

deBroglie wavelength is 1.807 angstrom