Introduction to Quantum Mechanics

Portland State University                                                                                                                                                                                                    Dr. Andres La Rosa
Fall 2026,  Sept 28th - Dec 12th                                                                                                                                                                            Email: andres@pdx.edu   ______________________________________________________________________________________________________________________________________________________  

          In the Fall-2026 term  quantum mechanics experiments with single photons will start to be
          implemented at Dr La Rosa's Lab.
                  -  Spontaneous parametric downcoversion.
                  -  Single photons exhibit quantum anticorrelation behavior: Proof of the existence of Photons.
                  - (Still in progress: Single Photon Interference.)
          These  modern experiments are updated versions of experiments outlined in LECTURE-6 of this course,
          " The PRINCIPLE of COMPLEMENTARY Quantum Behavior of Photons, Electrons and Atoms "
          (See figures 6.4 and 6.5 in that lecture.) ______________________________________________________________________________________________________________________________________________________  

Organization
          On campus lectures
                Room:  Vernier Science Center B1-15
                M & W 5:30-7:10 p.m.    

          Online office hours 
                Wednesday, 4:30 - 5:30 p.m.
                ZOOM Meeting ID:  279 107 2579  
                 
Nature and objectives of this course
This is a  theoretical course.      

We address the task of finding ways to describe the motion of particles without using the concept of trajectories ( r(t), v(t) ), as the later are incompatible with quantum mechanics (Heisenberg Principle).  So, we will rely on specific mathematical tools, like the "amplitude probability" (a complex number), which will guide us  to establish the Hamiltonian Equations (the "Newton's law for quantum states), which  governs  how a quantum state evolves with time.
While a more traditional introduction course would emphasize  on the calculation of a quantum state (i.e. finding the shape of  s, p, d,... orbitals), this course rather focuses on finding how the quantum state of a given physical problem evolves with time.  
This background will lead us to pursue  three main objectives of this course: 
1) To illustrate how the Hamiltonian Equations become the Schrodinger Equation.
2) To address the concept of  quantum entanglement (making quantitative calculation of the probabilities for particular process to
      happen in the decay of the positronium, while fulfilling the conservation of linear momentum, angular momentum and parity).
3) Detailed description of a quantum teleportation experiment (the quantum state  of a photon is teleported,  where  none of the
      operators is able to know the  teleported state.

Text

No specific textbook is required.
Students should be able to follow this course with any standard Quantum Mechanics textbook from the PSU Library (some are recommended below.)
It should be pointed out, however, that the Lecture Notes for this course closely follows the following three references:
-      Richard Feynman, “The Feynman Lectures on Physics,” Volume III, Addison Wesley, 1989.
        It is available free online: http://feynmanlectures.caltech.edu/III_toc.html 
        Feynman provides an intuitive and logical introduction to the QM ideas, instead of being a purely axiomatic reference.
-     Claude Cohen-Tannoudji, et al, "Quantum Mechanics" Vol I, John Wiley & Sons.
        This reference provides a comprehensive ,and more conventional, presentation of the QM theory.
        It consistently uses the brac-ket notation.         
- Mark Beck, Quantum Mechanics, Theory and Experiments, Oxford University Press, 2012. (Available online from the PSU LIbrary)
        It makes a modern presentation of QM theory, accompanied with guidance to   implement five QM laboratories that use single photon to
        demonstrate the existence of photons,  single-photon interference,  and quantum entanglement.
        Note:  In the Fall-2026 term, we will start presenting such interesting some of those laboratories (we have just started
                      purchasing the opto/mechanical components at this stage) , under the "Quantum Mechanics  Experiments with Single Photons" project.
                      (Ideally, we would have two, if not three, of such experiments ready to be shown to the class by the end of the term.) Two students from this class will be
                      hands-on participating in this project.

Other good references are:
      L. D. Landau and E. M. Lifshitz, “Quantum Mechanics (Non-relativistic Theory),” Butterworth Heinemann (2003).
      B. H. Bransdem and C. J. Joachin, "Quantum Mechanics," 2nd Ed. Prentice Hall.
      David Griffiths, "Introduction to Quantum Mechanics"; 2nd Edition, Pearson Prentice Hall.

For the classical Mechanics background, I have followed basically two books:
    Eugene Saletan and Alan H. Cromer, "Theoretical Mechanics," John Wiley, 1971;  and
    Herbert Goldstein, "Classical Mechanics," Addison-Wesley (1959).

Grading

Grading               400 level         500 level                             Deadlines

Midterm exam    35%                  30%                          Monday, November 2nd;    5:30-7:10 p.m.  

Homework           30%                  20%                          HW to be submitted electronically to:     boseeinsteincondensate2@gmail.com    

Project                                                20%                          Presentation (Optional) :  November, 18th, 2025
                                                                                                            Report:                                         November 25th, 2025

Final Exam     35%                   30%                     Monday,  December 7th,     5:30-7:10 p.m.  

       A     (95-100)    
      A-    (90-94)    
      B+   (85-89)    
      B      (80-84)    
      B-    (75-79)     
      C+   (70-74)    
      C     (65-69)    
      C-    (60-64)