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║ 18.11.2024 ║ Lecture 34 ║ |
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Problems ⯈ Some problems with solution on spin-1/2 particles |
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║ 14.11.2024 ║ Lecture 33 ║ |
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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. |
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║ 12.11.2024 ║ Lecture 32 ║ |
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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. |
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║ 11.11.2024 ║ Lecture 31 ║ |
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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) |
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║ 7.11.2024 ║ Quiz-2 ║ |
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║ 5.11.2024 ║ Lecture 30 ║ |
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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) |
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║ 4.11.2024 ║ Lecture 29 ║ |
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Solution to \( \theta,\phi \) part of Schrodinger equation ⯈ Solution to \( \theta,\phi \) part of Schrodinger equation (See sec 4.1 in Ref 3) ⯈ Visualising spherical harmonics ⯈ One more site for plotting spherical harmonics |
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║ 29.10.2024 ║ Lecture 28 ║ |
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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)). |
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║ 28.10.2024 ║ Lecture 27 ║ |
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Angular momentum algebra and operators ⯈ Solution to eigenvalue problem of \( L^2 \) and \( L_z \) (See sec 12.5 in Ref 1) |
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║ 24.10.2024 ║ Lecture 26 ║ |
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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 |
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║ 22.10.2024 ║ Lecture 25 ║ |
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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) |
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║ 21.10.2024 ║ Lecture 24 ║ |
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Cartesian to polar coordinates ⯈ Cartesian to polar coordinates in two-dimensions ⯈ Laplacian operator in polar coordinates in 2D |
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║ 17.10.2024 ║ Lecture 23 ║ |
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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) |
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║ 15.10.2024 ║ Lecture 22 ║ |
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Symmetries : ⯈ Rotational symmetry (see Sections 12.2 in Ref 1) ⯈ Invariance under rotation (see Sections 12.2 in Ref 1) |
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║ 14.10.2024 ║ Lecture 21 ║ |
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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) |
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║ 10.10.2024 ║ Lecture 20 ║ |
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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) |
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║ 8.10.2024 ║ Lecture 19 ║ |
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Symmetries : ⯈ Space translation symmetry in quantum systems (see Sec 11.1 and 11.2 in Ref 1) |
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║ 7.10.2024 ║ Lecture 18 ║ |
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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) |
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║ 3.10.2024 ║ Lecture 17 ║ |
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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 |
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║ 12.9.2024 ║ Lecture 16 ║ |
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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 |
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║ 10.9.2024 ║ Lecture 15 ║ |
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Uncertainty principle and relation : ⯈ Uncertainty relation for non-commuting variables (See sec 9.1 and 9.2 in Ref 1) |
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║ 3.9.2024 ║ Lecture 14 ║ |
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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) |
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║ 2.9.2024 ║ Lecture 13 ║ |
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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) |
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║ 29.8.2024 ║ Lecture 12 ║ |
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Harmonic oscillator : energy levels and eigenfunctions ⯈ Deriving harmonic oscillator solution (See sec 7.3 in Ref 1) |
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║ 27.8.2024 ║ Lecture 11 ║ |
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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 |
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║ 26.8.2024 ║ Lecture 10 ║ |
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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 |
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║ 22.8.2024 ║ Lecture 9 ║ |
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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 |
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║ 20.8.2024 ║ Lecture 8 ║ |
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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) |
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║ 19.8.2024 ║ Lecture 7 ║ |
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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. |
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║ 13.8.2024 ║ Lecture 6 ║ |
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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 |
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║ 12.8.2024 ║ Lecture 5 ║ |
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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 ? |
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║ 8.8.2024 ║ Lecture 4 ║ |
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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 |
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║ 6.8.2024 ║ Lecture 3 ║ |
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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) |
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║ 5.8.2024 ║ Lecture 2 ║ |
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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 |
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║ 1.8.2024 ║ Lecture 1 ║ |
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Brief review of classical mechanics, motivations for a theoretical framework beyond classical physics 🟤 Some historical notes on origins of quantum theory |
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