| Date |
Reading |
Problems |
Q&A |
| 05/13 |
Final Exam: Monday May 13, 8:00am(!!!). |
The exam will take place in the same room as all the lectures. Don't forget to bring a pen/pencil and a calculator. |
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05/09 |
Last lecture + review session for the final exam |
Bring your questions. Tentative equations sheets for the final exam are here. Don't forget to do the online course evaluation!!! |
Statistics of the current scores in this class will be posted below under Statistics. |
05/07 |
TSK Ch.14: 14.3, 14.5-8 {14.9} |
TSK Ch.14: Qs: 14.4,9,10. Prs: 4.13,14,26,27. Also follow the example problems in that chapter. Don't forget to submit your Graded HW #4 by 11:59 pm on Tuesday May 7. |
Answers/Solutions to graded HW #4 problems are here. |
| 05/02 |
TSK Ch.13 to the end; Ch. 15.4 (Entropy) |
Qs: 13.6,9,11. Prs: 13.9,10,14. Your graded Homework #4 (due by 11:59 pm on Tuesday May 7) is here. |
Answers/Solutions to Exam #2 problems and the current distribution of class scores are posted below ander Solutions and Statistics. Tentative equations for the upcoming final exam are here. |
| 04/30 |
Reading and problems from TSK (see Files on ELMS): Ch.13: 13.1-13.5, [Ch.12 -- refresher on probabilities].
Qs: 13.1-5; Pr: 13.1,7,12,19,20,27. 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!) (lecture slides, Equation 2 and also Ch. 12.3). For the latter, you might need Matlab or a similar program to assess the 1% accuracy level. |
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| 04/25 |
Midterm Exam #2 |
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04/23 |
Prepare for the midterm exam #2 |
Tentative equations sheet for the upcoming exam is here. Make sure you are familiar with these equations and which QM systems they correspond to. Recording of the review session for the upcoming Exam #2 has been posted on ELMS. |
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| 04/18 |
Ch.17.2-17.3. |
Ch.17: Ex. Pr: 17.1. Qs: 17.3, 17.14. Pr: 17.2. Recordings and lecture notes of two NMR lectures from a previous year have been uploaded to ELMS: look for files named BCHM485_NMR_Lecture_1 and BCHM485_NMR_Lecture_2.
Review session for the upcoming Exam #2 will be held via zoom on Tuesday April 23rd at 6pm. Bring your questions.
Tentative equations for the upcoming Exam #2 are here. Solutions to example problems from the previous year Exam #2 are here. |
If haven't done this yet, watch the educational YouTube video from the prevous lecture homework assignment. |
| 04/16 |
Ch.8.3-8.6,(8.8) and 17.1. |
Ch.8: Qs: 8.2,7,12,13,17; Prs: 8.2,8.7,8.40,8.41. Below is a link to educational YouTube videos illustrating basic aspects of Nuclear Magnetic Resonance which I will discuss in the next lecture. You want to watch video 01:
https://www.youtube.com/watch?v=7aRKAXD4dAg
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| 04/11 |
Ch.8: 8.6; the following sections were not covered today but please read: 8.3-8.5. |
Ch.8: Ex.Pr: 8.5-8.6; Pr: 8.35, 8,37. Verify by direct integration that transition dipole for μz (i.e. μ cos θ) between spherical harmonics with J=0 and J=1 is nonzero but between J=0 and J=2 is zero. Assume mJ=0. The equations for spherical harmonics can be found in Ch.7.7 and also on the Exam #1 equations sheets.
Example problems from the previous year Exam #2 are here. |
Solutions to graded HW #3 problems are here. |
| 04/09 |
Ch.8: 8.1-8.2, 8.9. |
Q: 8.4, Pr 8.47. Please note that -- as discussed in class -- the second midterm exam will be given on April 25th. |
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| 04/04 |
Ch.10: 10.2-10.3; 6.2; and 11.2, 11.4. |
Ch.10: Pr. 10.2,10.3,10.5.[10.4 -- for those who are curious about representing operators using matrices]. Determine the angle between the vector of electron spin and the z-axis.
For those who are curious about how to determine the eigenfunctions and eigenvalues of the Sx operator -- here is a detailed description of how to do this and how to answer the question about measuring Sx in the state described by the eigenfunction of the Sz operator.
For those who are curious about vector/matrix representations of the wavefunctions and operators -- here is an explanation with some examples.
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Answers/solutions to Exam #1 problems and the current distribution of the scores will be posted below under Exam #1 Solutions and Statistics. |
| 04/02 |
Ch.10.1,10.2,10.3 & 6.2, (ME 9) |
Ch.10: Qs: 10.1, 10.7. Prs: 10.7, 10.12, 10.13. Your graded Homework #3 (due by 11:59 pm on Monday April 8) is here. |
Answers/solutions to Exam #1 problems and the current distribution of the scores are posted below under Exam #1 Solutions and Statistics. |
| 03/28 |
Ch.9 to the end |
Ch.9: Ex.Pr: 9.4-9.6; Qs: 9.12,9.19; Pr: 9.15,9.25,9.23. Solve Exam #1 problems again, now without exam time pressure, and please read the problems and the questions carefully before solving them. |
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| 03/26 |
Ch.9: 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 (before the spring break). 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?
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Here are Exam #1 problems. As your (non-graded) homework assignment, do these problems again, now without time pressure. |
| 03/14 |
Ch.9: 9.1-9.3 |
Ch.9: Qs: 9.4,9.6,9.7,9.8,9.16. Pr: 9.2. Show by direct substitution into the equation for the radial part of the wave function (Eq. 9.5in 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 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? |
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| 03/12 |
Midterm Exam #1 |
Bring your calculator. |
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| 03/07 |
Prepare for the upcoming midterm Exam #1. Ch.7: 7.6, 7.8. |
Ch.7: Qs: 7.2-4,7.12,7.13; Pr: 7.35-37. (for those who know determinants: 7.34). Example problems from the previous year Exam #1 are here. Tentative equations sheet for the upcoming Exam #1 is here. Review sesssion in preparation for the midterm exam #1 will be held on Monday at 6 pm via zoom. Bring your questions. |
Answers & solutions to graded HW #2 problems are here. Answers/solutions to Exam 1 problems from the previous year are here. |
| 03/05 |
Ch.7: 7.5, 7.7 |
Ch.7: Qs: 7.9, 7.11; Pr: 7.31,7.32(a),7.33,7.36, 7.37. Review session for the upcoming midterm exam 1 will be held via zoom on Monday Marh 11 at 6 pm. Bring your questions. |
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| 02/29 |
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). Your graded Homework #2 (due on March 6) is here. |
For those who are curious: here I show how to calculate the probability to find quantum mechanical H.O. outside the allowed range for a classical H.O. |
| 02/27 |
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. |
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| 02/22 |
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]. Think of the Harry Potter and Platform 9 3/4 from last HW. |
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| 02/20 |
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. Two more problems:
1. Harry Potter and the Platform 9 3/4. Calculate the penetration length for Harry Potter using the model discussed in class to find out if the penetration through the wall phenomenon documented in this story is of Q.M. origin or is just magic. Repeat the same calculation but now for a proton, and for an electron. 2. Harry Potter and the Basilisk. Assume the Basilisk in the corridor is in the state described by the wavefunction of 1D PIB corresponding to n=4. Suggest a strategy that would allow H.P. to get trough the corridor without being bitten by the beast. |
Answers & solutions to graded Homework #1 problems are here. |
| 02/15 |
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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| 02/13 |
Ch.4: 4.2, 4.4 & Ch.2.1 |
Ch.4: Ex.Pr.4.1-4.4; Pr: 4.14,4.15,4.30,4.34, 4.35. Ch.2: Qs: 2.7,2.10. Your graded Homework #1 (due on Feb 19) is here. |
Some useful trigonometric identities and other formulae can be found here and on ELMS. |
| 02/08 |
Ch.4: 4.2. |
Ch.4: Qs: 4.2,4.9,4.11,4.12,4.14-15,4.18,20; Pr: 4.7,4.8,4.11,4.13, 4.16. |
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| 02/06 |
Ch.4: 4.1. |
Ch.4: Qs: 4.3-4.5; Pr: 4.1-3.
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| 02/01 |
Ch.3: to the end + Ch.2: 2.5,2.6. |
Ch.3: Pr: 3.11,3.12,3.16,3.19; Qs: 3.5,3.6-8.
A Schroedinger's cat problem: When opening the box, Schroedinger's cat was found alive in 64% experiments and dead in 36%. Based on these observations, reconstruct the wavefunction of the cat in the box. |
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| 01/30 |
Ch.2: 2.4,[2.5,2.6 -- prep. for next lecture]; Ch.3: 3.1-3.3 (+3.4, partially covered). |
Ch.2: Ex.Pr. 2.14; Pr: 2.13,2.14,2.20; Ch.3: Qs: 3.1-3.4,3.9; Pr: 3.1,3.2,3.9,3.10 |
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| 01/25 |
QCS: Ch.1 & Ch.2: 2.2; 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 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. |
A copy of today's slides has been placed on ELMS under Files. |
| before 01/25 |
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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