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What's coming in the next few classes |
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⯈ special topics : EPR and entanglement ⯈ special topics : Quantum algorithms (if time permits) ⯈ These special topics are for exposure and not part of exams. |
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17.4.2025 ║ Lecture 33 |
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EPR and entanglement 🟤 (not mandatory for the course) EPR paradox, Bell's theorem and entanglement (Sec 12.1, 12.2 in Ref 1) 🟤Alain Aspect’s historic experiments on Bell’s theorem 🟤A popular note on Bell's theorem and entanglement |
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15.4.2025 ║ Lecture 32 |
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Identical particles ⯈ Pauli exclusion principle and examples (Sec 10.3 in Ref 1) |
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7.4.2025 ║ Lecture 31 |
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Identical particles ⯈ Indistinguishability in quantum mechanics (Sec 10.3 in Ref 1) ⯈ Symmetric and anti-symmetric states (Sec 10.3 in Ref 1) |
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3.4.2025 ║ Lecture 30 |
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Fermi Golden Rule ⯈ Fermi Golden Rule for a band of final states ⯈ Fermi Golden Rule: brief notes (see towards the end) |
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1.4.2025 ║ Lecture 29 |
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Fermi Golden Rule ⯈ Fermi Golden Rule (Sec 18.2 in Ref 1) ⯈ Fermi Golden Rule: brief notes 🟤 (Extra reading, not necessary for the course) Applications of Fermi Golden rule |
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27.3.2025 ║ Lecture 28 |
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WKB approximation ⯈ WKB approximation : problems and examples ⯈ Using WKB method for energy of harmonic oscillator ⯈ WKB example problems |
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25.3.2025 ║ Lecture 27 |
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WKB approximation ⯈ WKB connection formula (Sec 8.3 in Ref 3, Ref 16.2 in Ref 1) ⯈ WKB connection formula: brief notes ⯈ WKB formula for bound state energy eigenvalues |
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24.3.2025 ║ Lecture 26 |
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WKB approximation ⯈ WKB approximation : tunnelling amplitude (Sec 16.2 in Ref 1) 🟤 (Extra reading, not necessary for the course) WKB approximation and Feynman's path integrals |
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20.3.2025 ║ Lecture 25 |
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WKB approximation ⯈ WKB approximation (Sec 16.2 in Ref 1) |
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18.3.2025 ║ Lecture 24 |
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Quantum scattering ⯈ Quantum scattering theory (Sec 11.1 to 11.3 in Ref 3) |
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17.3.2025 ║ Lecture 23 |
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Quantum scattering ⯈ Quantum scattering theory (Sec 11.1 to 11.3 in Ref 3) |
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13.3.2025 ║ Lecture 22 |
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Quantum scattering ⯈ Quantum scattering theory (Sec 11.1 to 11.3 in Ref 3) |
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11.3.2025 ║ Lecture 21 |
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⯈ Time dependent perturbation theory : problems ⯈ Some problems using perturbation theory |
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10.3.2025 ║ Lecture 20 |
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Approximation methods : Time dependent perturbation theory ⯈ See Lecture-29 for details ⯈ Periodic perturbations, Fermi Golden rule (Sec 18.2 in Ref 1) |
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6.3.2025 ║ Lecture 19 |
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Approximation methods : Time dependent perturbation theory ⯈ Problems in perturbation theory (Sec 18.1 and 18.2 in Ref 1) ⯈ Sudden and adiabatic perturbation (Sec 18.1 and 18.2 in Ref 1) |
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4.3.2025 ║ Lecture 18 |
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Approximation methods : Time dependent perturbation theory ⯈ Application of Time dependent perturbation theory (Sec 18.1 and 18.2 in Ref 1) ⯈ Sudden and adiabatic perturbation (Sec 18.1 and 18.2 in Ref 1) |
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3.3.2025 ║ Lecture 17 |
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Approximation methods : Time dependent perturbation theory ⯈ Time dependent perturbation theory (Sec 18.1 and 18.2 in Ref 1) |
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13.2.2025 ║ Lecture 16 |
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Approximation methods : Degenerate perturbation theory ⯈ Degenerate perturbation theory (Sec 6.2 in Ref 3) |
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11.2.2025 ║ Lecture 15 |
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Approximation methods : Perturbation theory ⯈ Problems for time-independent (non-degenerate) perturbation theory ⯈ Perturbation theory : problems with solution (Courtesy: Larry Sorenson, UW) |
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10.2.2025 ║ Lecture 14 |
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Approximation methods : Perturbation theory ⯈ Time-independent perturbation theory for non-degenerate case (Sec 17.1 in Ref 1) |
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6.2.2025 ║ Lecture 13 |
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Approximation methods : Variational technique (Sec 16.1 in Ref 1) ⯈ Variational technique and problems ⯈ Variational method applied to hydrogen atom |
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3.2.2025 ║ Lecture 12 |
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Computing Clebsch-Gordon (CG) coefficients ⯈ How to compute CG coefficients? ⯈ A problem to compute CG coefficients |
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30.1.2025 ║ Lecture 11 |
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Clebsch-Gordon (CG) coefficients (Sec 15.2 in Ref 1) ⯈ What are they and how to work with CG coefficients |
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28.1.2025 ║ Lecture 10 |
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Addition of general angular momenta (continued) ⯈ Listing the coupled basis states : \( |j ~ m, j_2 ~j_2\rangle \) (Sec 15.2 in Ref 1) ⯈ Solving in product basis \( |j_1 ~ m_1, j_2 ~m_2\rangle \) and coupled basis \( |j ~ m, j_1 ~j_2\rangle \) (Sec 15.2 in Ref 1) ⯈ Class notes for angular momentum addition |
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27.1.2025 ║ Lecture 9 |
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Addition of general angular momenta ⯈ Addition of two angular momenta (Sec 15.2 in Ref 1) ⯈ Listing the product basis states : \( |j_1 ~ m_1, j_2 ~m_2\rangle \) (Sec 15.2 in Ref 1) |
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23.1.2025 ║ Lecture 8 |
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Addition of two spin angular momenta (continued) ⯈ Addition of spin angular momenta (Sec 15.1 in Ref 1) ⯈ Solving in product basis \( |s_1 ~ m_1, s_2 ~m_2\rangle \) and coupled basis \( |s ~ m, s_1 ~s_2\rangle \). ⯈ Triplet and single states for addition of two spins. A quick recap of main result. ⯈ Symmetry properties of total-s states |
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21.1.2025 ║ |
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Class not held |
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20.1.2025 ║ Lecture 7 |
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Addition of two spin angular momenta ⯈ Addition of spin angular momenta (Sec 15.1 in Ref 1) |
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16.1.2025 ║ Lecture 6 |
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Coherent states ⯈ Coherent states of harmonic oscillator: Notes on coherent states (from UMD) ⯈ Coherent state in position representation |
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13.1.2025 ║ Lecture 5 |
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Periodic potential (continued) ⯈ Periodic potential (Sec 5.3.2 in Ref 3) |
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9.1.2025 ║ Lecture 4 |
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Periodic potential ⯈ Stern-Gerlach experiment (Example 4.4 in Ref 3) ⯈ Periodic potential (Sec 5.3.2 in Ref 3) |
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7.1.2025 ║ Lecture 3 |
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Spin dynamics ⯈ Dynamics of spin in external magnetic field, Larmor precession (Sec 14.4 in Ref 1, Sec 4.4.2 in Ref 3) |
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6.1.2025 ║ Lecture 2 |
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Spin dynamics ⯈ Spin dynamics and spin magnetic moment (Sec 14.4 in Ref 1) |
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2.1.2025 ║ Lecture 1 |
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How to handle exponential of an operator ⯈ Recalling some notations, and exponential of a Hamiltonian operator ⯈ How to sketch graphs : some simple examples |