| Date |
Reading |
Problems |
Q&A |
| 04/29 |
Ch.8: 8.6,8.9 |
Ch.8: Ex.Pr: 8.5-8.6; Qs: 8.15,8.17; 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 will be posted here. |
Solutions to graded HW #4 problems are here. |
| 04/24 |
TSK: Ch.14.1-2,15.4.2,15.5; QM: Ch.8: 8.1-8.2, 8.9. |
TSK: Ch. 15: Prs 15.25, 15.26. Q: 8.4. Do the homework problems from your previous assignments for Stat Thermodynamics. |
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| 04/22 |
TSK Ch.14: 14.4-14.5; Ch.15.2,6 |
TSK Ch.14: Qs: 14.6,7,9. Prs: 4.1-2,4-6,8,11,13,14,14. Also follow the example problems in that chapter. Calculate the thermal deBroglie wavelength for hydrogen atom and for molecular hydrogen at room temperature (T=300K).
Your graded Homework #4 (due by 11:59 pm on Monday April 28) is here. |
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| 04/17 |
TSK Ch.14: 14.3, 14.7-14.9; Ch.15.4 (Entropy) |
TSK Ch.14: Qs: 14.4,10,14-17. Prs: 4.26,27,33,34. Also follow the example problems in that chapter. |
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| 04/15 |
TSK Read Ch.13 to the end |
Do Ex.Prs: 13.3-13.5. Qs: 13.6,9-11. Prs: 13.9,10,13-14,22-24. Do the assessment, from the previous HW assignment, of the accuracy of Stirling's formula. |
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| 04/10 |
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. |
Solutions to graded HW #3 problems are here. |
| 04/07 |
Ch.10: 10.2-10.3; 6.2; and 11.2, 11.4. |
Ch.10: Pr. 10.2,10.5.[10.4 -- for those who are curious about representing operators using matrices]. Determine the angles that the vector of spin angular momentum of an individual electron can make with 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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| 04/03 |
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 Wednesday April 9) is here. |
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| 04/01 |
Ch.9 to the end |
Ch.9: Ex.Pr: 9.4-9.6; Qs: 9.12,9.19; Pr: 9.15,9.23-23. Calculate the average value of the potential energy of electron in the H atom in the 2s and n 2p states and compare your result with the total energy of the electron. Does the relationship = 2E that we obtained in class today for 1s electron hold for these states too? |
My answers/solutions to Exam #1 problems and the current distribution of the scores are posted below under Exam #1 Solutions and Statistics. |
| 03/27 |
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. 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 again. As your (non-graded) homework assignment, do these problems again, now without time pressure. |
| 03/25 |
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. |
The problems from your midterm Exam #1 are here. Please do these problems again and now pay attention to the hints (highlighted). |
| 03/13 |
Midterm Exam #1 |
Bring your calculator. |
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| 03/11 |
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). Recording of today's review session has been posted on ELMS. |
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| 03/06 |
Ch.7: 7.5, 7.7 |
Ch.7: Qs: 7.9, 7.11; Pr: 7.31, 7.32, 7.33, 7.36. Tentative equations sheet for the upcoming Exam #1 is here. Example problems from the previous year Exam #1 are here. Review session for the upcoming midterm exam 1 will be held via zoom on Tuesday Marh 11 at 6 pm. Bring your questions. |
Answers/solutions to graded Homework #2 are here. Solutions to example problems from the previous year Exam #1 are here. |
| 03/04 |
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). |
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: 7.2,7.7,7.9,7.10,7.14,7.16. Your graded Homework #2 (due on March 6) is here |
Answers/solutions to graded Homework #1 are here |
| 02/25 |
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]. |
|
| 02/20 |
Ch.5: 5.1-5.2, 5.5-5.6,(5.7) & Ch.2.1 (classical or quantum?) |
Ch.5: Qs: 5.6,5.8,5.13,5.14; Pr: 5.3. Ch. 2: Qs: 2.7,2.10.
Harry Potter and the Platform 9 3/4: Calculate the penetration length for Harry Potter using the "gravitational wall" 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. Assume m = 50 kg; v = 2 m/s; wall height H = 2m. Repeat the same calculation but now for a proton, and for an electron.
And don't forget to submit your graded HW=1. |
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| 02/18 |
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.
Think about the Harry Potter and the Basilisk question from the previous assignment: once you step into the quantum worlds, you become a wave. So, think about what your wavefunction should be given that you know the state/wavefunction of the Basilisk. Your graded Homework #1 (due on Feb 24) is here.
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| 02/13 |
Ch.4: 4.2 & 4.4 |
Ch.4: Ex.Pr.4.1-4.4; Qs: 4.9,11,14,15,18,19. Pr: 4.11,4.14,4.15,4.16,4.30,4.34,4.35. Determine the average (expectation) value of the momentum for a stationary state of a PIB by direct integration using the expectation value equation. 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 = 3. Suggest a strategy that would allow H.P. to get trough the corridor without being bitten by the beast. |
Some useful trigonometric identities and other formulae can be found here and on ELMS. |
| 02/11 |
Ch.4: 4.1, 4.2. |
Ch.4: Qs: 4.2-4.5, 20; Pr: 4.1-3, 4.7-8,12,13.
Show that the function Ψ(x)=b+exp(ikx) + b-exp(-ikx), where b+ and b- are arbitrady coefficients, is an eigenfunction of the energy operator for a free particle. What is the corresponding eigenvalue? |
|
| 02/06 (icy morning) |
Ch.3: to the end + Ch.2: 2.5,2.6. Recording of today's lecture and lecture notes have been posted on ELMS |
Finish doing end-of-chapter problems from the previous assignments.
Consider the following two wave functions: Ψ1=cos(kx) and Ψ2=sin(kx). Are they eigenfunctions of the kinetic enrgy operator? If yes, what is the eigenvalue? What value(s) of kinetic energy will you obtain in a single measurement and what as an average result of very many measurements? Answer the same questions for the momentum operator and the momentum measurements.
Do again the Schroedinger's cat problem, but in this case assume the cat was found alive in 81% experiments and dead in 19%. |
|
| 02/04 |
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). Refresh your knowledge of complex numbers. |
Ch.2: Example Pr. 2.4; 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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| 01/28 |
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 01/28 |
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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