Here are my solutions to various problems in David J. Griffiths’s excellent textbook *Introduction to Quantum Mechanics, Second Edition*. Obviously I can’t offer any guarantee that all the solutions are actually *correct*, but I’ve given them my best shot.

After some consideration, I’ve decided to repost this index to the solutions. I understand that some folks may be concerned that I am providing ‘free’ answers to problems that some students have been assigned as homework, but there are several points that should be made:

- First, solutions to the problems in Griffiths’s textbooks are already readily available on the internet, as a cursory search with Google will reveal, so I’m not giving away anything that isn’t easily obtained by other means. Many of these solutions are provided by professors for their own courses.
- If a teacher is concerned about students copying answers from the internet, s/he should consider making up their own problems. I did this for the courses that I taught in my 25 years as a university lecturer. For a field as rich as physics, it shouldn’t be too difficult to come up with original problems.
- If you’re a student seeking to copy solutions, you should realize that you won’t learn much unless you make a genuine effort to solve the problem on your own first. Remember that in most universities, the majority of the marks for a course are obtained from exams, and if you sit an exam without having worked out problems on your own beforehand, your chances of passing are pretty low. In my experience as a teacher myself, I found that most students realize this and do make a genuine effort to learn the material on their own.
- Finally, judging by many comments I have received, my posts have provided many readers with different (and hopefully in many cases, clearer) explanations of sometimes difficult concepts, so their value goes beyond merely providing solutions to a few textbook problems. In most of my posts, I have tried to provide an explanation of the theory behind the problem in a way that makes sense to me, which usually involves filling in steps sometimes omitted in the textbooks.

There is an official site listing errata in the textbook. If you’re confused by something in the text itself, it’s worth having a look here to see if there is a typo on that page.

**Chapter 1 – The Wave Function**

1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18

**Chapter 2 – Time-Independent Schrödinger Equation**

2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17a, 2.17b-d, 2.18, 2.19, 2.20, 2.21, 2.22, 2.23, 2.24, 2.25, 2.26, 2.27, 2.28, 2.29, 2.30, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, 2.39, 2.40, 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.48, 2.49, 2.50, 2.51, 2.52, 2.53, 2.54, 2.55, 2.56, 2.56 (extra)

**Chapter 3 – Formalism**

3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.10, 3.11, 3.12, 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20, 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, 3.29, 3.30, 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.37, 3.38, 3.39, 3.40

**Chapter 4 – Quantum Mechanics in Three Dimensions**

4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, 4.19, 4.20, 4.21, 4.22, 4.23, 4.24, 4.25, 4.26, 4.27, 4.28, 4.29, 4.30, 4.31, 4.32, 4.33, 4.34, 4.35, 4.36, 4.37, 4.38, 4.39, 4.40, 4.41, 4.42, 4.43, 4.44, 4.45, 4.46, 4.47, 4.48, 4.49, 4.50, 4.51, 4.52, 4.53, 4.54, 4.55, 4.56, 4.57, 4.58, 4.59, 4.60, 4.61

**Chapter 5 – Identical Particles**

5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12, 5.13, 5.13d, 5.14, 5.15, 5.16, 5.17, 5.18, 5.19, 5.20, 5.21, 5.22, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, 5.29, 5.30, 5.31, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37

**Chapter 6 – Time-independent Perturbation Theory**

6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 6.10, 6.11, 6.12, 6.14, 6.15, 6.16, 6.17, 6.18, 6.19, 6.20, 6.21, 6.22, 6.23, 6.24, 6.25, 6.26 (weak field), 6.26 (strong field), 6.26 (general case), 6.27, 6.29, 6.30, 6.31, 6.32, 6.33, 6.34, 6.35, 6.36, 6.37, 6.38, 6.39, 6.40

**Chapter 7 – The Variational Principle**

7.1, 7.2, 7.3, 7.4, 7.5, 7.7, 7.8, 7.9, 7.10, 7.11, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, 7.19, 7.20

**Chapter 8 – The WKB Approximation**

8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 8.10, 8.11, 8.12, 8.13, 8.14, 8.15a, 8.15b-f, 8.16, 8.17

**Chapter 9 – Time-Dependent Perturbation Theory**

9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, 9.10, 9.11, 9.12, 9.13, 9.14, 9.15, 9.16, 9.17, 9.18, 9.19, 9.20, 9.21a, 9.21b-c, 9.22

**Chapter 10 – The Adiabatic Approximation**

10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.8a-d, 10.8e-f, 10.9, 10.10

**Chapter 11 – Scattering**

11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, 11.9, 11.10, 11.11, 11.12, 11.13, 11.14, 11.15, 11.16, 11.17, 11.18, 11.19

Mudasra KanwalThis is a best problem site which has helped me lot. in understanding physcs especially quantum mechanics

emmanuelThis site is superb, thanks to the originators.

emmansonuelSuperb site, Thanks to the originator(s)

tsahhi i am looking for the solution for problem 2.17 in the second edition. can you help me>

growescienceI have already posted this – see above.

ChristianYou have no idea how much your website has helped me. Thank you so much.

AnonymousHelpful to read longer and thoroughly explained answers – thank you

Lam Wing SumGreat thanks!!!

asaddude splended job i am reallygrateful to you

asad

asadagain thanks dude

YoungPhysicistThanks so much, this site is super helpful! Really clear explanations :).

JackWhen I tried to copy some of the solutions into Microsoft Word, a few equations are not displayed on Word, and I have to manually drag in from IE into Word.

Is there something wrong with my Word?

growescienceI don’t use Word so I can’t check, but copying into LibreOffice Writer does seem to work, although the formatting isn’t great.

Keep in mind that each equation is actually a hyperlink to an image, so in order to display it, Word needs to

retrieve it from the web.

Anonymouswouldn’t have gotten through quantum mech without this site. Thanks so much!

sumit deyThank god!! Prof glenn is back with his set of the clearest solutions. i as a student will always be grateful to him for the clear cut conceptual way of handling physics problems. Thank u Sir.

GaryI’m a former astronomy research who has gotten into education. I needed to refresh my basic physics, so this site has proven wonderful. Thank you.

ElliotGreat help for any student trying to learn quantum mechanics, keep it up and thank you

OliverWonderful job! These explanations are so much better than those of Griffiths who skips over half of the answer in my opinion

growescienceThanks. I always try to put in enough explanation so I can understand it myself when I go back to it in 6 months…

SteveHey, just wanted to let the owner know, that this site is great, I’m an undergraduate studying physics and this site has helped me alot, i am looking for the derivation of the expectation value for (1/r^3) for the spin orbit term of the fine structure of the hydrogen atom. You gave the solution but you said you will post the derivation later, but i can’t seem to find it anyway. Many many thanks

growescienceThe derivation you’re looking for is here. I’ve updated the page to include the link.

For info, you can see which of my later articles refer back to the post you’re looking at by looking at the “Trackbacks” at the bottom of each page.

NANGOYE DEOi’m going to college to persue Bsc.Educ(physics and mathematics) so will i meet these concepts anywhere in the course and please guide me on how to handle this course ( which chapters should i master first) because i have never been to college before

gwrowePost authorI can’t really offer any advice as I don’t know what courses you will be taking. If your degree is in education, and you’re training to be a high school teacher, though, I wouldn’t think you will meet much of what’s on physicspages (at least not with as much mathematics as I’ve used), as my blog is aimed at the intermediate university level. It would be best to ask your college what’s in their courses.

Sir Physics StudentThis website is extremely helptfull. Everything is explained very clearlery.

CJThis is superb. As an engineer getting a dual degree in physics this has helped me decipher the difference in math between the subjects.

shuaiWhere is the problem 9.23–problem 9.26？ Thanks a lot!

shuaiI found them. My version is a little different. It’s the international version. Thanks!

PolThank you very much for this! Thank you! Thank you! and Thank you!

Benjamin CordesThis has really helped me. Thank you so much for making this available.

Hira jamilRealy happy to find solution of those problms which i cnt solv myslf

Thank u so much to shear these sol here…

John from ASUThis site is the only reason I graduated with a firm understanding of the material. Bravo

JoshThis is great!!!!

Amin Yahya Zethanks a lot bro

Tanner JacksonThese questions are out of order from the second edition

gwrowePost authorThey are all in the correct order for my copy of the second edition.

pavithraM looking for solution of problem number 1.20….. can i get the solution for that problem???

gwrowePost authorThere are only 18 problems in chapter 1.

SofiaThank you very much not only for the solutions but also for the other posts! They are superb, keep up the good work.

Nikos C.I have to add my sincere thanks to whoever took the time to solve these problems from D. Griffiths’ book and post them so neatly. It has been tremendously helpful to people like me who decided to learn QM in his old age. This is much appreciated.

Francisco PhamThank you and nice work, Dr. Rowe.

FangHeartfelt thanks are in order — as someone trying to get a grasp of quantum mechanics all on my own with books as my only teachers, these solutions you have provided are incredibly helpful. Because until I found these, I was hesitant to solve problems on my own, what with having no way to verify my work, and no way to get a hint on how to proceed in case I got stuck.

While the concerns about such neatly worked out solutions being freely available are valid insofar as students getting lazy and/or not doing their homework, I think the benefit is far too much to take them off. Besides, any true student of quantum mechanics knows/realizes well enough that the only real way to learn quantum mechanics is to “do” it – a thought Griffiths himself espouses in the very beginning! 🙂

Anyway, quite the ramble that was. Hopefully I will also have time to peruse the rest of your rather interesting looking blog. Thanks very much once again, and wish you a great year ahead!

SamuelYou are the best. Those quantum problem are just difficult sometimes, and you are sharing this solution with everybody. Thank you.

Kirsten BaleHi! I just wanted to extend the sincerest of thank you’d to you for the solutions you’ve provided here. I am deeply grateful, as they have helped me to complete my quantum mechanics assignments (which I previously found so baffling I felt I had no hope of finishing them) in a timely manner, but, more to the point, your solutions are set up in such a way that they have enabled me to develop a genuine understanding of the material. You have struck such a marvellous balance between providing enough information to guide me through my work, without providing so much that I don’t have to actively engage in the material. I am enjoying my course much more than I was at the beginning of the semester, and feel that I have gained a meaningful understanding of the material. Thank you so much.

gwrowePost authorThank you for the kind words. It’s always gratifying to find that my blog is helping someone else through what can be a difficult subject.