Lecturer:   Masud Haque   (haque@thphys.nuim.ie)

Lectures and Tutorials

Lecture schedule:   (1) Wednesdays 09:05, JHL7.   (2) Fridays 12:05, Hall D (Arts Block).

Tutor:   Aonghus Hunter-McCabe  

Problem sets

Problem set 11.   Was due on Friday, December 18th.
Some hints/remarks/solutions for Problem set 11.

Problem set 10.   Was due on Friday, December 11th.
Some hints/remarks/solutions for Problem set 10.

Problem set 09.   Was due on Friday, December 4th.
Some hints/remarks/solutions for Problem set 09.

Problem set 08.   Was due on Friday, November 27th.
Some hints/remarks/solutions for Problem set 08.

Problem set 07.   Was due on Friday, November 20th.
Some hints/remarks/solutions for Problem set 07.

Problem set 06.   Was due on Friday, November 13th.
Some hints/remarks/solutions for Problem set 06.

Problem set 05.   Was due on Friday, November 6th.
Some hints/remarks/solutions for Problem set 05.

Problem set 04.   Was due on Friday, October 23rd.
Some hints/remarks/solutions for Problem set 04.

Problem set 03.   Was due on Friday, October 16th.

Problem set 02.   Was due on Friday, October 9th.

Problem set 01.   Was due on Friday, October 2nd, at the end of the first week of semester.

Problem bank

Here is a large collection of problems, which I call `problem set 12'.

You would probably benefit from working on some of these problems.

Handouts: some notes/comments

A listing of the basic rules (`postulates') of quantum mechanics.

The formal definition of hermitian conjugates.

Averaging continuous vs discrete variables.

A discussion of one way to think of wavefunctions as vectors.

Probability densities versus probability amplitudes versus just probabilities.

Measurement of a spin-1/2 object.

Scanned lecture notes

Scanned lecture notes, part A.

Scanned lecture notes, part B.

Scanned lecture notes, part C.

Scanned lecture notes, part D.

Scattering off a negative potential step.

Scanned lecture notes, part E.

Scanned lecture notes, part F.

Textbooks and other Sources

Quantum mechanics is counter-intuitive. There will be confusing aspects; you will need to invest time and effort to clear up these confusions.

Do not expect to get comfortable with QM unless you do a fair amount of reading and problem-solving.

It is strongly recommended that you work through one or more texts. Working through Prof. Nash's lecture notes is an absolute minimum. It would be a very good idea to read a couple of sections every week.
Additional texts are listed below, and there are links to lecture notes etc. There are many textbooks on introductory quantum mechanics (e.g., carried by the Maynooth library, physically and as e-books). Textbooks have differences in ordering and notation, but you should benefit by reading any text.

Please let me know if any of the links below are broken.

Overviews of Introductory Quantum Mechanics:

• MP363 lecture notes of Prof. Charles Nash
  Please aim to understand ALL of the material in these notes. The class will not follow the ordering but you are expected to pick up all concepts at the level of these notes.
• A summary of the basic principles: Essentials of Quantum Mechanics.
  These are basic principles that you should make sure you understand and absorb. E.g., item 4 tells you about measurement.
• A concise introduction to Q.M.:   Textbook chapter from a book by D. Morin ,
  This covers (roughly) a subset of the material of Nash's notes. You could use it as a secondary reading source. You are expected to digest all the material here.
• Quantum mechanics of a single particle on a line:   Chapter titled `Quantum Mechanics in 1D', from some lecture handouts.
• Quantum mechanics of a single particle on a line:   A chapter titled `Wave mechanics', from some lecture notes.
• Wikipedia's Introduction to Quantum Mechanics does not describe the formalism, but describes many important concepts.
• Wikipedia page on ``Wave function''.
• Wikipedia page on Schroedinger equation.
• Wikipedia page titled ``Mathematical formulation of quantum mechanics''.

Dirac notation (bra-ket notation) and properties of bra's and ket's:

Please get comfortable with this mathematical formulation. Chapter 2 of Nash notes introduces most of the notation. Here are some more references:

• Wikipedia pages:   page on Bra-Ket notation and page on orthonormal basis.

• Notes P. Kok. The first chapter summarizes bra-ket notation, operators, etc. Try digesting the first three sections.
  (The rest of the notes are rather advanced.)

• Overview of the Mathematical Formalism of QM, from notes of Bertlmann.

• From the notes of J.Cresser: for the mathematical formalism, try Chapter 8, Chapter 9, and Chapter 10,

• On bra-ket notation:   A chapter titled `Dirac's Bra and Ket Notation', from some lecture notes.

Spin-1/2 systems:

This topic is not covered in Nash's notes. We will use the spin-1/2 system for many examples; so it is important that you get familiar through other sources. Some links below.

• Link 1:   Notes on Spin-1/2 systems.   Please read Sections 2 and 3 at least.

• Link 2:   A Chapter on Spin-1/2 systems and Pauli matrices.

Postulates of Quantum Mechanics:

Not covered in Nash's notes. The numbering of postulates varies (is not standardized), but each treatment covers very similar statements.

• Link 1:   Notes by Jaffe, MIT.
  The postulates are discussed in section 1 of these notes.

• Link 2:   Wikipedia.

The Dirac delta function:

• Notes on the delta function from various people:
  a link,   another link,   another link,   another link,   another link.   another link.

• Wikipedia page on the delta function.

• If the potential experienced by a particle has the form of a dirac delta function, you can solve for the bound states as well as the scattering states:
  Wikipedia page on the Dirac delta potential in quantum mechanics.
  Another link covering the topic.

  You are expected to be able to calculate properties of the bound state and also calculate transmission and reflection coefficients for scattering states.

Sources for other topics:

• Two slit inteference:
  Here is a careful description of two-slit interference.
  Please read through: this topic is not covered in Nash's notes.

• Wikipedia article on `Wave-particle duality'. Includes discussion and animation of interference.

• Review of the Birth of Quantum Mechanics (from lecture notes by M.Fowler).
  This nicely supplements Chapter 1 of Nash's notes.

• From notes of J.Cresser: Early History of Quantum Mechanics

• Useful wikipedia pages: momentum operator; position operator; Schroedinger equation; Self-adjoint (hermitian) operator; Unitary operator; Uncertainty principle.

Textbooks:

There are many textbooks available on introductory quantum mechanics. I list some sources below.
(I omit publisher and year of publication: the author and title should be enough to identify each textbook.)

• Volume III of The Feynman Lectures on Physics ; can be read online.

• D. J. Griffiths, Introduction to Quantum Mechanics.

• D. A. Miller, Quantum Mechanics for Scientists and Engineers.

• M. Beck, Quantum Mechanics: Theory and Experiment.

• J. S. Townsend, A Modern Approach to Quantum Mechanics.

Notes on Exam

The exams are TWO HOURS long.

The exam will NOT have a choice of M questions out of N, as was common a few years ago.
You will be asked to answer ALL questions.

Assignment marks (`continuous assessment') will be counted toward the final module mark only if they are to the students' advantage.
(The policy is module-dependent and varies within the Theoretical Physics department. In some modules, continuous assessment is `compulsory'.)

Previous Exams

Here are solutions to repeat exam for 2017-2018 (August 2018 exam).

Here are solutions to the January 2018 finals.

Here are solutions to repeat exam for 2016-2017 (August 2017 exam).

Here are solutions to the January 2017 finals.

Continuous Assessment

Assignments (solutions to problem sets) are to be uploaded electronically via the moodle page. Hopefully, you are used to this procedure from the last part of the Spring 2020 semester.
(The drawer system for submitting assignments has been suspended due to the pandemic.)

We may not be marking all the assignments. This means, some assignments will go un-marked, but we will not announce beforehand which. Also, for those assignments which are marked, we might mark either the complete assignment, or some fraction selected randomly.

The primary purpose of the problem sets is really that they should help you learn quantum mechanics at an optimal rate. It will be assumed that you are attempting every problem set including the problems marked [SELF]. If you are comfortable doing all the problems including [SELF]'s during the week and then want to tackle additional problems, please let me know with a brief email and I will send you some further optional problems to work on.