# 9: Quantum Mechanics¶

## Example number 9.1, Page number 202¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
V = 100;     #Accelerating potential for electron(volt)

#Calculation
lamda = math.sqrt(150/V)*10**-10;     #de-Broglie wavelength of electron(m)

#Result
print "The De-Broglie wavelength of electron is",lamda, "m"

The De-Broglie wavelength of electron is 1.22474487139e-10 m


## Example number 9.2, Page number 203¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
e = 1.6*10**-19;     #Energy equivalent of 1 eV(J/eV)
h = 6.626*10**-34;    #Planck's constant(Js)
m = 9.11*10**-31;     #Mass of the electron(kg)
Ek = 10;     #Kinetic energy of electron(eV)

#Calculation
p = math.sqrt(2*m*Ek*e);     #Momentum of the electron(kg-m/s)
lamda = h/p ;     #de-Broglie wavelength of electron from De-Broglie relation(m)
lamda = lamda*10**9;     #de-Broglie wavelength of electron from De-Broglie relation(nm)
lamda = math.ceil(lamda*10**2)/10**2;     #rounding off the value of lamda to 2 decimals

#Result
print "The de-Broglie wavelength of electron is",lamda, "nm"

The de-Broglie wavelength of electron is 0.39 nm


## Example number 9.4, Page number 203¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
h = 6.626*10**-34;      #Planck's constant(Js)
m = 9.11*10**-31;       #Mass of the electron(kg)
v = 1.1*10**6;     #Speed of the electron(m/s)
pr = 0.1;        #precision in percent

#Calculation
p = m*v;     #Momentum of the electron(kg-m/s)
dp = pr/100*p;    #Uncertainty in momentum(kg-m/s)
h_bar = h/(2*math.pi);     #Reduced Planck's constant(Js)
dx = h_bar/(2*dp);         #Uncertainty in position(m)

#Result
print "The uncertainty in position of electron is",dx, "m"

The uncertainty in position of electron is 5.26175358211e-08 m


## Example number 9.5, Page number 203¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
e = 1.6*10**-19;     #Energy equivalent of 1 eV(J/eV)
h = 6.626*10**-34;    #Planck's constant(Js)
dt = 10**-8;      #Uncertainty in time(s)

#Calculation
h_bar = h/(2*math.pi);    #Reduced Planck's constant(Js)
dE = h_bar/(2*dt*e);       #Uncertainty in energy of the excited state(m)

#Result
print "The uncertainty in energy of the excited state is",dE, "eV"

#answer given in the book is wrong

The uncertainty in energy of the excited state is 3.2955020404e-08 eV


## Example number 9.6, Page number 204¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
c = 3*10**8;      #Speed of light(m/s)
lamda = 400;    #Wavelength of spectral line(nm)

#Calculation
lamda = lamda*10**-9;      #Wavelength of spectral line(m)
#From Heisenberg uncertainty principle,
#dE = h_bar/(2*dt) and also dE = h*c/lambda^2*d_lambda, which give
#h_bar/(2*dt) = h*c/lambda^2*d_lambda, solving for d_lambda
d_lamda = (lamda**2)/(4*math.pi*c*dt);     #Width of spectral line(m)

#Result
print "The width of spectral line is",d_lamda, "m"

The width of spectral line is 4.24413181578e-15 m


## Example number 9.14, Page number 207¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
a = 2*10**-10;    # Width of 1D box(m)
x1=0;    # Position of first extreme of the box(m)
x2=1*10**-10;   # Position of second extreme of the box(m)

#Calculation
def intg(x):
return ((2/a)*(math.sin(2*math.pi*x/a))**2)

The probability of finding the electron between x = 0 and x = 10**-10 is 0.5