615.654.81 - Quantum Mechanics

Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the left menu. Each module may be divided into more than one video, and includes a homework assignment. Modules become available on Saturdays at 1 AM EST.  Late assignments will have their maximum attainable grade reduced by 10% for the first 3 late days, 20% for the next 3, and 50% for later than 6 days.   Extension requests will be considered on a case by case basis.  If you are asked to resubmit for a higher grade then the re-submission must occur within 2 days of the posted grade; grades are usually posted 10 days of submission.

Course Topics

• Historical introduction to light and wave-particle duality (black-body radiation, photoelectric effect, Compton scattering, the double-slit experiment including the delayed-choice experiment, beam-splitters and mirrors, quantum bomb tester), quantum computers and the Deutsch algorithm, electron diffraction and de Broglie matter waves, Bohr's theory of electron in Hydrogen atom. Classical mechanics and the old quantum theory of Wilson-Sommerfeld (including the relativistic correction).

• The Schrodinger wave equation, wave packets for a free particle, localized potentials in one spatial dimension, quantum tunneling, Kronig-Penney potential, Bloch’s theorem and the band structure of metals, linear operators, quantum observables, expectation values and uncertainties, commutation relations, the uncertainty principle, time-energy uncertainty relation, general solution to the Schrodinger wave equation for stationary Hamiltonians, periodic potentials, the JWKB approximation and alpha-decay.

• Stationary states, angular momentum operator and spherical harmonics, electrical multipole operators, Schrodinger's equation in an external electromagnetic field, gauge invariance, the Aharonov-Bohm effect.  The propagator, the Feynman path integral formulation of quantum mechanic, Heisenberg and Schrodinger pictures, constants of motion, Ehrenfest’s theorem, the Virial theorem.
  
• Quantum theory of scattering:  the Green function, the scattring amplitude, the Optical theorem, the Born approximation, the Eikonal approximation, partial wave analysis, low-energy scattering.
  
• The Dirac notation, postulates of quantum mechanics, time-reversal and parity operators, Hilbert space of states, linear operators, exponential of operators, the BCH theorem, the state projection operator, tensor-product Hilbert spaces, the measurement problem, the density operator, pure and mixed states, entangled states, the Schmidt decomposition.

• The Harmonic oscillator, application to heat capacity of solids, Landau quantization, coherent states.

• The normal Zeeman effect, magnetic moment of electrons in atoms, the Stern-Gerlach experiment and electron spin, eigenvalues of general angular momentum operators, Pauli 2-component theory of spin, Symmetry and angular momentum algebra, the rotation group and angular momentum operators, non-Abelian Lie groups, representations of the rotation group, the groups SO(3) and SU(2).

• Spin wave functions and their rotations,  addition of angular momentum operators, Clebsch-Gordan coefficients, the Wigner-Eckart theorem, EPR paradox and Bell’s theorem.

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• Identical particles, the exchange force, the Helium atom, the shell model of heavy atoms, the periodic table, quantum statistical mechanics: Fermions and Bosons, free-electron model of metals, white dwarfs, the Bose-Einstein condensation and the lambda-transition point of He4, black-body radiation.

• Time-dependent perturbation theory and the semi-classical theory of radiation, quantized electromagnetic field, Mach-Zehnder interferometer, quantum optics.
  

Course Goals

To achieve a high level of proficiency of the formalism and concepts of modern quantum theory in order to be able to enter into all application areas such as atomic and nuclear physics, physical chemistry, and quantum information processing.

Course Learning Outcomes (CLOs)

• Describe the historically important experiments that led to the development of the old and the new quantum theory.
• Demonstrate how to construct wave packets and the mathematical formalism underlying modern quantum mechanics and the Dirac notation.
• Solve the time-independent Schrodinger wave equation with some special potentials (e.g., sectionally constant potentials, the delta-function potential and the harmonic oscillator potential) in 1 dimension.
• Analyze the Schrodinger wave equation in 3 dimensions using the angular momentum operator formalism, and learn to analyze quantum systems with intrinsic spin.
• Analyze and solve problems related to the principles of quantum statistical mechanics.
• Apply approximation techniques, e.g., perturbation theory, variational principle, and the JWKB method to specific quantum mechanical problems.
• Analyze problems related to quantum scattering.
• Understand and be able to perform sophisticated mathematical operations related to multiple quantum systems, tensor product Hilbert spaces, entangled states, operators defined on tensor product Hilbert spaces, and the density operator.

Textbooks

This course is meant to be self-contained.  However, it is highly recommended that you obtain the textbook “Introduction to Quantum Mechanics (3rd edition)”, by David J. Griffiths and Darrell F. Schroeter for additional examples and explanations.

Student Coursework Requirements

It is expected that each module will take approximately 7–14 hours per week to complete. The lectures will take between 2-4 hours.  I expect you to read relevant sections from the recommended text or your preferred online sources for about 2-3 hours.  The assignments should take 3-7 hours. This course will consist of three basic student requirements:

1. Discussion - Preparation and Participation (10% of Final Grade Calculation): 

   Module discussions are a great source of interaction with everyone in the class.  Official discussion topics will be available for some, and not all, modules. Discussions take place using the “Discussion” thread. Discussions should be thoughtful and not simply a repetition of what someone else has already discussed. If the discussion relates to the most difficult topic of the module then you are expected to describe the issue and references you have found helpful in resolving the issue, including the details.  If you find no topic particularly hard then pick one and describe how you might explain it to someone in your class and add any insights in addition to what you have learnt in this class.  I will monitor module discussions and respond when necessary.  If your discussion is flagged as inadequate you have 2 days to resubmit for full credit. 

   
   
2. Assignment - Homework problems (80% of Final Grade Calculation):  Assignment (homework problems) will be relevant to the learning objectives and will be assigned a numerical value with a maximum of 100.  The final grade will be based on 14 equally weighted homework problem sets.  All assignment must be submitted as PDF files in Canvas.  The preferred method of producing your PDF file is LaTex, but you can use word processing software (such as Word) with ability to write equations.  If your handwriting is excellent and very legible then you can submit PDF versions of well scanned pages (as ONE file); cell phone photos of handwritten pages are often unacceptable because of bad lighting, viewing angle, and size. Late submissions will be reduced when prior arrangements have not been made.  If the work is late and you have not spoken with me prior to submitting your work, the maximum grade you could achieve is reduced by 10% for the 1st 3 years, 20% for the next 3 days, and 50% for later.  Assignment grades will be available within 7-10 days after submission.  Multiple attempts will be granted when deserved; should you be asked to make a second attempt then you must submit your second attempt within 2 days so as to receive full credit.
   

3. An oral final zoom interview (10% of Final Grade Calculation):  A short (2-5 minute) oral examination conducted via ZOOM.  No special preparation or access to notes is necessary.

Final grade is based on the following percentages:

Grading Policy

See Course Schedule for due dates.  All assignments must be submitted in PDF format on Canvas. Students are encouraged to use LaTex, Word, or equivalent environments to produce a PDF output for submission; handwritten and scanned PDF outputs must be legible (handwritten pages photographed on your phone on the kitchen table are unacceptable). Late assignments will have their maximum attainable grade reduced by 10% for the first 3 late days, and 20% for the next 3 late days, and 50% for later days.  Extension requests for extenuating circumstances will be considered on a case by case basis.  If you are asked to resubmit for a higher grade then the resubmission must occur within 2 days of the posted grade.

The course grading scale is the following:

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.