Homework

Homework files  to be submitted to:   unionizinggradiation@gmail.com
                                                                                  (with copy to  andres@pdx.edu )
                                                                                                                                                                                        Due date:

Homework 1
Complex variable Phasors Divergence Rotational                                                                          10-03-2022
            Hint for question 4A
            Complementary information
            Complex numbers    Brief compendium of complex variable                                       Reading assignment
            The necessity of complex numbers to describe quantum mechanics                    (Ref: MIT Lecture QM )        
                  Nature works with complex numbers, no with real numbers                              
            Representation of travelling harmonic waves in complex variable: PHASORS
            Plane Waves 
            How the complex numbers were invented                                                                               (Interesting video)
                            This presentation shows how by giving up math connection to reality
                            (i.e. by accepting areas of negative values) scientist ended up discovering
                            a deeper truth of how the real world works (i.e the Shrodinger Eq. infact
                            uses complex numbers in its formulation.)

(Optional)
          Amplitude probability (photons)                                                                                                                  (Subject no covered in 2023) 
            Hint for question #1            Complementary information             Helpful  approximations: Taylor expansions            The variational principle is treated in more detail in Chapter-4, Section 4.1.
            Section 26-6 in: Feynman Lectures, Vol-I, Chapter 26,   "Optics: The Principle of Least Time."
(Optional)
          Finding the Lagrangian for a particle in an E&M field                                                                   
(Optional)                                                                                                                                                                  
        Atom modeled as an harmonic oscillator; Planck's hypothesis of quantized energy

Homework 2                                                                                                                                                          10-10-2023
Spectral decomposition of wavefunctions into a base   

Homework 3                                                                                                                                                        10-17-2023                   
Wavefunction describing the motion of a free particle: scalar product; delta Dirac   
            Solution to question 1Aa

Homework 4                                                                                                                                                       10-24-2023
Bracket notation; Amplitude probability; 2 versions of Hamiltonian Eqs

Homework 5                                                                                                                                                             10-31-2023
Bra-ket notation, Free ammonia molecule, Ammonia molecule under
Static field,  Hamiltonia expressed in different basis

(Optional)                                                                                                                                                       
Hamiltonian in different Base, general 2x2 Hamiltonian, modification of the energy  levels       

Homework 6                                                                                                                                                             11-14-2023                                                             
Ammonia molecule interacting with a time-dependent electric field                                 

Homework 7                                                                                                                                                             11-21-2023                                                                                                                                     
Dynamics of an electron in a lattice crystal that has one defect         

Homework 8                                                                                                                                                             11-28-2023    
Quantum Entanglement  

Homework 9                                                                                                                                                            12-05-2023                                                                                                                                                         
QM operators, expectation values