2-QM Reminders
                      Eigen value of L2 operator
• Presented by:Yasir Iqbal
• Presented to:Sir zahid Mehmoud
• Roll No:17257
• Session:2017-2021(BS Physics)
• Semester:7th
• Department of physics,Govt.Sadiq Egerton 
• College BWP
 Sketch of Quantum Physics
Quantum 
 Failure of physics
Classical Wavefunction
physics   Bohr 
Theory
 Schrindinger 
 Photoelectric effect equationsQuantum 
numbers
 Planck’s Hypothesis
 Black body  Conpton 
radiation scattering  Hydrogen  Particles 
  Energies Wave particle Duality
 hydrogen  Forces
 Radiation curve  Spectrum  Applications
 Uncertainity Principle Atomic
 Wein Displacement Law  properties  Atomic
 structure
 Periodic
 Quantum Statistics  3k Background  Table  Molecular
Radiation  Structure
Outline
•  Eigen value of angular momentum operator
•  Spherical polar coordinates
•  variable seperable method
•  Apply chain rule 
•  Take trigonometric equation
•  Compare solution with legender polynomial equation
•  Take a terminating series for a definite solution
• Results
Common Operators
• Position
 r = ( x, y, z )    - Cartesian repn
• Momentum
p   i    i ( x , y , z )
• Total Energy
E optot  i t
• Angular Momentum
L = r x p     - work it out
Using Operator L2Z
Suppose L2Z   is an operator when operates
On a wavefunction       gives eigen value 
which is as follow:                             
     
                        L2z     ………….(1)
 the original wavefn
 a constant
(as far as A is concerned)
Suppose L2 is an operator which operates on wavefuctioon Ψ gives 
the value of λ.
                       

Suppose L2 is an operator which operates on wavefuctioon Ψ gives 
the value of λ.
                       





Thank you