| Date |
Reading |
Problems |
Q&A |
| 04/16 |
TSK Read Ch.13 to the end. Also: Ch.15.4 (entropy) |
Do Ex.Prs: 13.3-13.5. Qs: 13.6,9-11. Prs: 13.9,10,13-14,22-24. Perform the assessment, from the previous HW assignment, of the accuracy of the Stirling's formula. |
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| 04/14 |
Reading and problems from TSK (see also Files on ELMS): Ch.13: 13.1-13.5, [Ch.12 -- refresher on probabilities]. |
Qs: 13.1-5; Pr: 13.1,6,7,12,,27. Using your calculator find the smallest value of n for which the Stirling's formula (see lecture slides, Equation 1) approximates the value of n! within 10% accuracy, 1% accuracy.
Do the same for ln(n!) (see Equation 2 in lecture slides on ELMS and also Ch. 12.3). For the latter, you might need Matlab or a similar program to assess the 1% accuracy level. |
|
| 04/09 |
Ch.10.1,10.2,10.3 & 6.2, (+ME 9) |
Ch.10: Qs: 10.1, 10.7. Prs: 10.2, 10.3, 10.7, 10.12, 10.13. Your graded Homework #3 (due by 12:00 pm on Friday April 17) is here. |
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| 04/07 |
Ch.9 to the end; Ch. 10.1, and ME9 |
Ch.9: Ex.Pr: 9.4-9.6; Qs: 9.12,9.19; Pr: 9.15,9.23-25. Calculate the average value of the potential energy of electron in the H atom in the 2s state and compare your result with the total energy of the electron. Does the relationship < V > = 2E that we obtained in class today for 1s electron hold for these states too? Calculate the average distance, < r >, from the nucleus for 1s electron, and compare 1/< r > with < 1/r >. |
My answers/solutions to Exam #1 problems are posted below under Exam #1 Solutions and Statistics. |
| 04/02 |
Ch.9: 9.2-9.3-9.4 |
Ch.9: Ex.Pr: 9.1-9.3; Qs: 9.5,9.6,9.10,9.15,9.18. Do the HW assignments from the previous lecture. Calculate and compare the energies of electrostatic interaction and gravitational interaction between electron and proton. What is the degeneracy of the state(s) of H atom with the principal Q.N. n? For 2s and for 2pz orbitals determine the points in the 3-D space where there is the highest probability to find the electron.
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| 03/31 |
Ch.9: 9.1-9.2 |
Ch.9: Qs: 9.8. Pr: 9.2. Show by direct substitution into the equation for the radial part of the wave function (Eq. 9.5 in the textbook) that R(r) = A*exp(-r/a) is a solution to Shroedinger Equation for H-atom when l = 0; determine the values of a and E. Calculate and compare the energies of the electrostatic interaction and the gravitational interaction between electron and proton. |
|
| 03/26 |
Ch.7: 7.6, 7.8. |
Ch.7: Qs: 7.2-4,7.12,7.13; Pr: 7.28,7.31-32, 7.35-38. Prove that the operator of the square of the angular momentum, l^2 = lx^2+ly^2+lz^2, commutes with lx and ly and lz. For this you might want to use the commutators of lx, ly and lz -- see your lecture notes or Equations (7.63) from the textbook.
Also, by performing the integration as we did in class, verify that the normalization coefficients for rank-2 (l = 2) spherical harmonics in Equations (7.65) in the textbook are correct (do it for a couple of harmonics). |
A video recording and accompanying handwritten notes from a similar lecture given in 2021 are available on ELMS under Files -- look for filenames that contain "L13_2021". |
| 03/24 |
Ch.7: 7.5, 7.7 |
Ch.7: Qs: 7.9, 7.11; Pr: 7.31, 7.32, 7.33, 7.36. |
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| 03/12 |
Midterm Exam #1 |
Bring your calculator. |
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| 03/10 |
Prepare for the midterm exam. After the exam: Ch.6: 6.1,6.3,6.4 |
Ch.6: Example Prs: 6.1, 6.3-6.5. Qs: 6.5,6.8,6.13,i6.14,6.18. Pr: 6.1,6.3,6.6,6.7,6.13,6.20. Prove the genearal relationships for the commutators which I gave you in class. Specifically, evaluate the commutator [A,BC]. |
Answers/solutions to HW #2 problems are here. |
| 03/05 |
Ch 7: 7.2, 7.4, Math Essential 7 & 8 |
Ch.7: Ex.Pr.: 7.4,7.5. Qs: 7.10,7.19. Pr: 7.25,7.27,
7.32(b). Tentative equations sheet for the upcoming Exam #1 is here
Review session for the upcoming midterm exam #1 will be held via zoom on Tuesday March 10 at 7 pm. Bring your questions! |
Example problems from the previous year Exam #1 are here.
Answers/solutions to these problems are here. Please look at them only after you solved or attempted to solve the problems yourself. |
| 03/03 |
Ch 7: 7.1,7.3 |
Ch.7: Qs: 7.1,7.5,7.7; Ex.Pr: 7.2,7.3; Pr: 7.2,7.7,7.9,7.10,7.14,7.16. Your graded Homework #2 (due on March 10) is here
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Answers/solutions to graded Homework #1 are here |
| 02/26 |
Ch.5: 5.1-5.2, 5.5-5.6,(5.7) |
Ch.5: Qs: 5.6,5.8,5.13,5.14; Pr: 5.3.
Harry Potter and the Platform 9 3/4: Using the "gravitational wall" model discussed in class calculate the penetration length for (1) a proton and (2) an electron. Assume velocity v = 2 m/s; wall height H = 2m.
And don't forget to submit your graded HW#1. |
|
| 02/24 |
Ch.4: 4.3; Ch.5: 5.3 |
Ch.4: Pr: 4.19-21, 4.23, 4.24, 4.27; Ch.5: Pr: 5.1, 5.2.
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| 02/19 |
Ch.4: 4.2 & 4.4, also 2.1 |
Ch.4: Ex.Pr.4.1-4.4; Qs: 4.9,11,14,15,18,19. Prs: 4.14,4.15,4.16,4.30,4.34,4.35.
Harry Potter and the Basilisk Problem. Assume the Basilisk in the corridor is in the state described by the wavefunction of 1D PIB corresponding to n = 3. Suggest a strategy that would allow H.P. to get trough the corridor (from one end to another) without being bitten by the beast.
Your Graded HW #1 (due on Feb 27) is here. |
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| 02/17 |
Ch.4: 4.2 (& 4.1) |
Ch.4: Prs: 4.7, 4.8, 4.11, 4.13. |
Some useful trigonometric identities and other formulae can be found here and on ELMS. |
| 02/12 |
Ch.4: 4.1. |
Ch.4: Qs: 4.4,4.5; Pr: 4.1-3. Also do previously assigned end-of-chapter problems. Video recording of a similar lecture (it was Lecture 5) from 2021 was posted on ELMS together with the lecture notes. |
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| 02/10 |
Ch.3: to the end + Ch.2: 2.2,2.5,2.6. |
Ch.3: Qs: 3.10-12; Prs: 3.11,3.13,3.21. Finish doing end-of-chapter problems from the previous assignments. |
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| 02/05 |
Ch.3: to the end + Ch.2: 2.5,2.6. |
Ch.3: Qs: 3.4,3.5,3.6-8; Pr: 3.1,3.2,3.9,3.12,3.19,3.20,3.22.
A Schroedinger's cat problem: When opening the box, Schroedinger's cat was found alive in 64% of experiments and dead in 36%. Based on these observations, reconstruct the wavefunction of the cat in the box. |
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| 02/03 |
Ch.3: 3.1-3.3; Ch.2: 2.4, [2.5 -- prep. for next lecture]. Refresh your knowledge of complex numbers (ME 6). |
Ch.2: Pr: 2.13,2.14,2.17,2.19,2.20; Ch.3: Qs: 3.1,3.2 |
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| 01/29 |
Snowday. QCS: Ch.1 & ME 6 |
Ch.1: Do Example problem 1.3 from Ch.1: determine the radius of the lowest-energy orbit of electron in Bohr's planetary model of the hydrogen atom. Do Numeric Problem 1.15.
Using Wien's displacement law, λmax*T=1.44/5 cm*K, perform the following calculations:
(1) estimate λmax for your body radiation, and
(2) assuming that the maximum amount of Sun's radiation is in the yellow range, i.e. λmax ~ 580 nm, estimate the temperature of the Sun's surface.
It's not too late to prepare yourself for the course. The relevant information can be found below and also on ELMS. |
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| 01/27 |
Snowday. Watch video recording and lecture notes of lecture # 1 from year 2021 posted on ELMS under Files. |
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| before 01/27 |
Prepare yourself for the course. The relevant information can be found
here. |
Pepare yourself for the course. The relevant information can be found here. |
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