phy321 : quantum mechanics

PH 3124 : Quantum Mechanics I
(August-December, 2024)

This is a first course on non-relativistic quantum mechanics.

Course contents :

Mathematical formalism, vector spaces, states and operators
Experimental motivations, postulates of quantum mechanics
uncertainty principle and its consequences
Time-independent and time-dependent Schrodinger equation
One dimensional problems
Central potential, angular momentum and spin
Hydrogen atom problem
Charged particle in electromagnetic field
Bell's inequality and entanglement

Books :

NOTE 1 : The first two books in this list can be downloaded legally within IISER Pune.
NOTE 2 : Ref 1, 2, 3 in the updates (given below) refer to these text books.

Principles of quantum mechanics by R. Shankar
Quantum mechanics : An Introduction by Walter Greiner
Introduction to quantum mechanics by David Griffiths

Evaulation :

Class tests : 40 %
Midsem : 30 %
Final : 30 %

Office hours :

Wednesdays 5 - 6 PM (Room A-321)
Saturdays 9.15 AM to 10 AM (Room A-382)

Announcements :
🖈 Aug 14, 2024 : Quiz-1 will be held on 5.9.2024 during 9 to 10 AM.
Everything taught in class until 27.8.2024 will be part of this test. Harmonic oscillator not part of the test.

🖈 Sep 12, 2024 : Quiz-1 :Question paper and Solution

🖈 Sep 12, 2024 : For mid-semester exam, everything taught in class until 12.9.2024 (lectures 1 to 16) will be part of the exam.

🖈 Oct 10, 2024 : Quiz-2 will be held on 7.11.2024 during 9 to 10 AM. Everything covered in lectures 17 to 25 will be part of this quiz.

🖈 Oct 22, 2024 : Midsem exam : Question paper and Solution

🖈 Nov 10, 2024 : Quiz 2 : Question paper and Solution

🖈 Nov 18, 2024 : End-sem exam : Everything covered in lectures 1 to 34 will be part of this exam. However, 75% of the questions will be from the part taught after mid-sem exam (lectures 17 to 34).

🖈 Dec 6, 2024 : Endsem exam : Question paper and Solution

Assignments / problem sheets :

🖈 Aug 26, 2024 : Assignment-1 (Try out these sample problems)
🖈 Nov 4, 2024 : Assignment-2 (Try out these sample problems)
🖈 Nov 5, 2024 : Sample problem set-1 with solutions (By Bharathi Kannan)
🖈 Nov 10, 2024 : Sample problem set-2 with solutions

COURSE UPDATES :

NOTE 1 : Course updates will appear here.
NOTE 2 : Ref 1, 2, 3 refer to the text book list given above.
NOTE 3 : 🟤 Brown circle indicates that the content is for extra reading and not necessary for this course.

║ 18.11.2024 ║ Lecture 34 ║
Problems ⯈ Some problems with solution on spin-1/2 particles

║ 14.11.2024 ║ Lecture 33 ║
Spin ⯈ Pauli matrices and their properties, (See Sec 14.3 in Ref 1) ⯈ Spin operators about arbitrary direction, (Sec 14.3 in Ref 1) ⯈ Representing an arbitrary $2 \times 2$ matrix in terms of Pauli matrices, (Sec 14.3 in Ref 1, and see this example problem) ⯈ Rotation operators for spins (See sec 14.3 in Ref 1) 🟤 (Extra reading, not mandatory for the course) Quantum particles are not spinning: historical notes on spin.

║ 12.11.2024 ║ Lecture 32 ║
Spin ⯈ Stern-Gerlach experiment, ⯈ electron spin, ⯈ Spin operators and algebra (See sec 14.3 in Ref 1) ⯈ Pauli spin matrices (See sec 14.3 in Ref 1, OR sec 4.1.1 in Ref 3) 🟤 Lasting impact of Stern-Gerlach experiment. 🟤 Stern-Gerlach : How a bad cigar changed atomic physics. 🟤 Do your own Stern-Gerlach experiment here.

║ 11.11.2024 ║ Lecture 31 ║
Solving Hydrogen atom problem ⯈ Solution to radial Schrodinger equation for Hydrogen atom potential : eigenstates (See sec 13.1 in Ref 1, OR sec 4.2 in Ref 3)

║ 7.11.2024 ║ Quiz-2 ║

║ 5.11.2024 ║ Lecture 30 ║
Solving Hydrogen atom problem ⯈ Solution to radial Schrodinger equation for Hydrogen atom potential : energy eigenvalues (See sec 13.1 in Ref 1, OR sec 4.2 in Ref 3)

║ 4.11.2024 ║ Lecture 29 ║
Solution to $θ, ϕ$ part of Schrodinger equation ⯈ Solution to $θ, ϕ$ part of Schrodinger equation (See sec 4.1 in Ref 3) ⯈ Visualising spherical harmonics ⯈ One more site for plotting spherical harmonics

║ 29.10.2024 ║ Lecture 28 ║
Angular momentum algebra ⯈ Explicit matrix forms for $J_{x}, J_{y}, J_{z}, J_{+}, J_{-}$ and $J^{2}$ . (See sec 12.5 in Ref 1) ⯈ Spherical polar coordinates ⯈ Schrodinger equation in spherical coordinates 🟤 (Extra reading, but not necessary for the course) Orbital angular momentum (OAM) of photons 🟤 Quantum computing using OAM of a single photon (J. Opt. 13 064022 (2011)).

║ 28.10.2024 ║ Lecture 27 ║
Angular momentum algebra and operators ⯈ Solution to eigenvalue problem of $L^{2}$ and $L_{z}$ (See sec 12.5 in Ref 1)

║ 24.10.2024 ║ Lecture 26 ║
Dealing with angular momentum in three dimensions ⯈ Angular momentum in three-dimensions (See sec 12.4 in Ref 1) ⯈ Deriving angular momentum commutators ⯈ Angular momentum commutators

║ 22.10.2024 ║ Lecture 25 ║
Two-dimensional harmonic oscillator ⯈ Solving 2D oscillator (See also exercise 12.3.7 in Section 12.4 of Ref 1) ⯈ A little more detailed solution to 2D oscillator ⯈ Note : Most of the standard 2D rotationally invariant problems can be solved in a similar way as the 2D harmonic oscillator. ⯈ Some pictures of 2D oscillator eigenstates (make your own eigenstate)

║ 21.10.2024 ║ Lecture 24 ║
Cartesian to polar coordinates ⯈ Cartesian to polar coordinates in two-dimensions ⯈ Laplacian operator in polar coordinates in 2D

║ 17.10.2024 ║ Lecture 23 ║
Solving rotationally invariant problems : $z$ -component of angular momentum ⯈ Solving for eigenstates of $L_{z}$ operator (see Section 12.3 in Ref 1) ⯈ A sample problem (see Section 12.3 in Ref 1) ⯈ Consistency checks of composition of rotation and translation operations (see end of Sec 12.2 in Ref 1)

║ 15.10.2024 ║ Lecture 22 ║
Symmetries : ⯈ Rotational symmetry (see Sections 12.2 in Ref 1) ⯈ Invariance under rotation (see Sections 12.2 in Ref 1)

║ 14.10.2024 ║ Lecture 21 ║
Symmetries : ⯈ Parity symmetry (see Sections 11.4 in Ref 1) ⯈ Time reversal invariance (see Sections 11.5 in Ref 1) ⯈ Generalising space translation to two-dimensions (Sec 12.1 in Ref 1)

║ 10.10.2024 ║ Lecture 20 ║
Symmetries : ⯈ space and time translation symmetry (see Sections 11.2 and 11.3 in Ref 1) ⯈ Parity symmetry (see Sections 11.4 in Ref 1)

║ 8.10.2024 ║ Lecture 19 ║
Symmetries : ⯈ Space translation symmetry in quantum systems (see Sec 11.1 and 11.2 in Ref 1)

║ 7.10.2024 ║ Lecture 18 ║
Dirac delta potential : ⯈ Dirac delta potential (scattering potential) (see Sec 2.5 in Ref 3) 🟤 Optical frequency combs (Combs are a series of delta functions)

║ 3.10.2024 ║ Lecture 17 ║
Dirac delta function and Dirac delta function potential : ⯈ Dirac delta function ⯈ An easy to read article on Dirac delta function ⯈ Dirac delta function potential [bound states] (see Sec 2.5 in Ref 3) 🟤 Extra reading (but not necessary for the course) : History of Dirac delta function

║ 12.9.2024 ║ Lecture 16 ║
Minimum uncertainty wavepacket and applications of uncertainty principle : ⯈ Applications of uncertainty relation (See sec 9.3 and 9.4 in Ref 1) ⯈ Consequences of commuting and non-commuting observables ⯈ Time-dependent Schrodinger equation and time evolution of states

║ 10.9.2024 ║ Lecture 15 ║
Uncertainty principle and relation : ⯈ Uncertainty relation for non-commuting variables (See sec 9.1 and 9.2 in Ref 1)

║ 3.9.2024 ║ Lecture 14 ║
Harmonic oscillator : Evaluating matrix elements of operators, comparison with classical ⯈ Evaluation of matrix elements (See sec 7.4 in Ref 1) ⯈ Comparison with classical probability (See sec 7.4 in Ref 1) ⯈ Computing eigenstates in position basis (See sec 7.5 in Ref 1)

║ 2.9.2024 ║ Lecture 13 ║
Harmonic oscillator : raising and lowering operators, solution in energy basis ⯈ Solution in energy basis using raising/lowering operators (See sec 7.4 in Ref 1)

║ 29.8.2024 ║ Lecture 12 ║
Harmonic oscillator : energy levels and eigenfunctions ⯈ Deriving harmonic oscillator solution (See sec 7.3 in Ref 1)

║ 27.8.2024 ║ Lecture 11 ║
Ehrenfest theorem, Commutator, Harmonic oscillator ⯈ Ehrenfest theorem and conditions under which it is valid (Chapter 6 in Ref 1) ⯈ Harmonic oscillator (See sec 7.3 in Ref 1) ⯈ Commutators (See sec 7.3 in Ref 1), ⯈ Evaluation of position-momentum commutator

║ 26.8.2024 ║ Lecture 10 ║
Quantum tunnelling and its applications, Ehrenfest theorem, commutator ⯈ See tunnelling applications: radioactive decay and STM ⯈ Ehrenfest theorem (See Chapter 6 in Ref 1). 🟤 Extra reading (but not necessary for the course) : Is quantum tunnelling faster than light ? 🟤 Extra reading (but not necessary for the course) : The future of semiconductor industry

║ 22.8.2024 ║ Lecture 9 ║
Completeness of eigenstates of infinite well, solution to step potential, potential barrier problem ⯈ Completeness of eigenstates (see (4) in sec 2.2 of Ref 3). This is a general property, not just of eigenstates of infinite well system. ⯈ Step potential in one-dimension (Sec 5.4 in Ref 1). ⯈ Potential barrier in one-dimension

║ 20.8.2024 ║ Lecture 8 ║
General properties of one-dimensional quantum systems ⯈ No degeneracy in 1D quantum systems (see sec 5.6 in Ref 1), symmetry properties, orthonormal eigenstates. ⯈ Probability current density (See sec 5.3 in Ref 1)

║ 19.8.2024 ║ Lecture 7 ║
Infinite square well potential, its eigenvalues and eigenfunctions ⯈ Infinite well problem (see Sec 5.2 in Ref 1 given above) ⯈ Classical infinite well problem; comparing with quantum results. Correspondence principle.

║ 13.8.2024 ║ Lecture 6 ║
Hermitian operator and its properties, orthogonal eigenfunctions, completeness relation, solving the free particle Schrodinger equation, momentum eigenfunction ⯈ Hermitian operators and properties (see Sec 3.2 and 3.3 of Ref 3 given above) ⯈ Momentum eigenfunctions (see Sec 3.3 of Ref 3) ⯈ Free particle solution in quantum mechanics

║ 12.8.2024 ║ Lecture 5 ║
Postulates of quantum mechanics, Schrodinger equation, real eigenvalues. ⯈ Postulates of quantum mechanics [measurement postulate and time-evolution] (See chapter 4 of Ref 1 listed above) ⯈ Time-dependent and time-independent Schrodinger equation ⯈ Hermitian operator and real eigenvalues 🟤 Extra reading (but not necessary for the course) : Is the Schrodinger equation true ?

║ 8.8.2024 ║ Lecture 4 ║
Postulates of quantum mechanics, Hilbert space, Bra-ket notation, operators, average value of operators, states and operators in different representations. ⯈ Defining Hilbert space ⯈ Bra-ket notation for starters ⯈ Bra-ket notation and postulates (pages 1-6) ⯈ Class notes on momentum operator

║ 6.8.2024 ║ Lecture 3 ║
phase and group velocity of DeBroglie wave, plane waves, Davisson-Germer experiment, Born's interpretation, superposition principle, Postulates of quantum mechanics ⯈ Phase and group velocity of DeBroglie waves (See Section 3.1 of Ref 2 given above)

║ 5.8.2024 ║ Lecture 2 ║
Wave particle duality, Double-slit experiment, De Broglie waves and its consequences Actual double-slit experiment with electrons (Courtesy : Hitachi Co., 1989) 🟤 See also : The accompanying paper on this double-slit experiment

║ 1.8.2024 ║ Lecture 1 ║
Brief review of classical mechanics, motivations for a theoretical framework beyond classical physics 🟤 Some historical notes on origins of quantum theory

Back to home page