||Final Exam: Monday May 15, 8:00am(!!!).
||The exam will take place in the same room as all the lectures.
||Last lecture + review session for the final exam
|| Bring your questions. Tentative equations sheets for the final exam are here.
|| Statistics of the current scores in this class can be found below under Statistics.
||TSK Ch.14.1-2,10, 15.2,4,5,6
|| TSK Ch.15: Prs: 15.3, 15.12, 15.13. Tentative equations sheets for the final exam are here.
||Answers/Solutions to graded HW #4 problems are here.
||TSK Ch.14: 14.3-9
|| TSK Ch.14: Qs: 14.4,9,10. Prs: 14.1,4.13,26,27. Also follow the example problems in that chapter. Don't forget to submit your Graded HW #4 by 11:59 pm on Monday May 8.
||TSK Ch.13 to the end; Ch. 15.4 (Entropy)
||Qs: 13.6,9,11. Prs: 13.8,10,14. Your graded Homework #4 (due by 11:59 pm on Monday May 8) is here.
||Midterm Exam #2
||After the exam: 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.
|| Answers/Solutions to Exam #2 problems and the current distribution of class scores are posted below ander Solutions and Statistics.
||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. Review session for the upcoming Exam #2 will be held via zoom on Tuesday, April 25, at 5pm. Use the same zoom link as for office hours.
|| Ch.17: Es. Pr: 17.1. Qs: 17.3, 17.14. Pr: 17.2. If you haven't done this yet, watch the educational YouTube video from the prevous lecture homework assignment. My solutions to Exam #2 problems from the previous year are posted here. I strongly recommend that you try solving these problems yourself before looking at my soluitions.
|| Solutions to graded HW #3 problems are here.
||Ch.8.3-8.6,8.8 and 17.1.
|| Ch.8: Qs: 8.13,8.17; Prs: 8.37,8.40. 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.
|Example problems from the previous year Exam #2 are here.
||Ch.8: 8.6; the following sections were not covered today but please read: 8.3-8.5 [8.7].
||Ch.8: Ex.Pr: 8.2-8.6; Qs: 8.2,8.6,8.7,8.10,8.12; Pr: 8.2,8.7, 8.18, 8.15.
||Ch.8: 8.1-8.2, 8.9.
||Q: 8.4, Pr 8.47
||Don't forget to submit your graded HW#3 which is due on April 12.
||Ch.10: 10.2-10.3; and 6.2.
||Ch.10: Pr. 10.2,10.3,10.5.[10.4 -- for those who are curious about representing operators using matrice]. Determine the angle between the vector of electron spin and the z-axis.
Determine the eigenfunctions and eigenvalues of the Sy operator -- you can follow the example of Sx eigenfunctions derivation that we did in classi and also a detailed description, posted here , of how to determine eigenfunctions of the Sx operator 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.
Your graded Homework #3 (due by 11:59 pm on Wednesday April 12) is here.
|Answers/solutions to Exam #1 problems and the current distribution of the scores are posted below under Solutions and Statistics.
|| Ch.10.1 + 10.2-10.3 & 6.2
|| Ch.10: Qs: 10.1, 10.7. Prs: 10.7, 10.12, 10.13. Here is a copy of Exam #1 sheets. Solve these problems again, now without exam time pressure, and please read the problems and the questions carefully before solving them.
||Ch.9 to the end
|| Ch.9: Ex.Pr: 9.4-9.6; Qs: 9.12,9.19; Pr: 9.5, 9.13, 9.15,9.23,9.25. Calculate the average potential energy of 2p and 2s electrons and assess if the relationshiop = 2*En which we obtained in class for the 1s electron still holds.
|| 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?
||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.
||Midterm Exam #1
|| Bring your calculator.
||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). Review sesssion in preparation for the midterm exam #1 will be held on Friday at 5 pm via zoom. Bring your questions. Tentative equations sheet for the upcoming Exam #1 is here
||Answers/solutions to Exam 1 problems from the previous year are here.   |
||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. Example problems and equations sheet from the previous year Exam #1 are here.
Review session for the upcoming midterm exam 1 will be held via zoom on Friday at 5 pm.
Bring your questions.
|| Answers & solutions to graded HW #2 problems are here.  |
||Ch 7: 7.2, 7.4
||Ch.7: Ex.Pr.: 7.4,7.5. Qs: 7.10,7.19. Pr: 7.25,7.27,
|| 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.
||Ch 7: 7.1,7.3, Math Essential 7 & 8
||Ch.7: Qs: 7.1,7.5,7.7; Ex.Pr: 7.2,7.3; Pr: 7.2,7.7,7.9,7.10. Your graded Homework #2 (due on March 6) is here.
||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]. Do the Harry Potter and Platform 9 3/4 from last HW.
||Ch.5: 5.1-5.2, 5.6-5.8
||Ch.5: Qs: 5.6; Pr: 5.3. Two more problems:
1. Harry Potter and the Platform 9 3/4 problem. 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 related to Q.M. or is just magic. Repeat the same calculation but now for a proton, and for an electron. 2. 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=5. 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.
|| 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.
||Ch.4: 4.2, 4.4 & Ch.2.1
||Ch.4: Ex.Pr.4.1-4.4; Pr: 4.14,4.16,4.20,4.34. Ch.2: Qs: 2.7,2.10. Your graded Homework #1 (due on Feb 20) is here.
||Some useful trigonometric identities and other formulae can be found here and on ELMS.
||Ch.4: Qs: 4.2,4.9-10,4.12,4.14-15,4.18-20; Pr: 4.5,4.7,4.8,4.11,4.13.
||Ch.4: Qs: 4.3-4.5; Pr: 4.1,4.2.
||Ch.3: 3.1-3.5 (all) + Ch.2: 2.5,2.6.
||Ch.3: Pr: 3.11,3.19; Qs: 3.1,3.5,3.6,3.8-3.10.
Question: When opening the box, Schroedinger's cat was found alive in 64 out of 100 experiments and dead in 36. Based on these observations, reconstruct the wavefunction of the cat in the box.
Question: How can you tell from the outcome of your experiments if the QM system is in a pure state or in a superposition state?
||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: 3.1,3.2,3.9,3.10
|| 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.
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 as well as recording of Lecture 1 from 2021 have been placed on ELMS under Files.
|| Prepare yourself for the course. The relevant information can be found
|| Pepare yourself for the course. The relevant information can be found here.