Griffiths – Introduction to Quantum Mechanics problems

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.

These solutions are the only ones that I’ve worked out so far, so please don’t ask me to post “the rest of the chapters” as I haven’t worked on those yet. I will get to them eventually.

Chapter 1 – The Wave Function

1.71.13, 1.14

Chapter 2 – Time-Independent Schrödinger Equation

2.1, 2.2, 2.3, 2.42.5, 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, 2.202.21, 2.22, 2.232.24, 2.25, 2.262.27, 2.28, 2.29, 2.30, 2.312.32, 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

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, 3.203.21, 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, 4.374.38, 4.39, 4.40, 4.41, 4.42, 4.43, 4.44, 4.45, 4.464.47, 4.48, 4.49, 4.50, 4.51, 4.52, 4.53, 4.54, 4.55, 4.56, 4.57, 4.584.59, 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, 5.315.32, 5.33, 5.345.35, 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, 6.96.10, 6.11, 6.12, 6.146.15, 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, 6.386.39, 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, 8.88.9, 8.10, 8.11, 8.12, 8.13, 8.14, 8.15a, 8.15b-f, 8.168.17

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, 9.189.19, 9.209.21a, 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

Chapter 11 – Scattering

11.1

Comments

  • Mudasra Kanwal  On Monday, 4 March 2013 at 17:29

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

  • emmanuel  On Saturday, 11 May 2013 at 16:38

    This site is superb, thanks to the originators.

  • emmansonuel  On Saturday, 11 May 2013 at 16:39

    Superb site, Thanks to the originator(s)

  • tsah  On Sunday, 29 September 2013 at 09:00

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

    • growescience  On Sunday, 29 September 2013 at 09:12

      I have already posted this – see above.

  • Christian  On Thursday, 19 December 2013 at 19:45

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

  • Anonymous  On Thursday, 1 May 2014 at 11:52

    Helpful to read longer and thoroughly explained answers – thank you

  • Lam Wing Sum  On Saturday, 24 May 2014 at 01:53

    Great thanks!!!

  • asad  On Thursday, 5 June 2014 at 11:57

    dude splended job i am reallygrateful to you
    asad

  • asad  On Monday, 29 September 2014 at 05:42

    again thanks dude

  • rodolfo2  On Wednesday, 26 November 2014 at 06:11

    Thank you!

  • YoungPhysicist  On Friday, 5 December 2014 at 03:52

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

  • Jack  On Thursday, 11 December 2014 at 06:59

    When 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?

    • growescience  On Friday, 12 December 2014 at 09:39

      I 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.

  • Anonymous  On Tuesday, 16 December 2014 at 22:57

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

  • sumit dey  On Saturday, 21 February 2015 at 10:27

    Thank 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.

  • Gary  On Wednesday, 4 March 2015 at 06:03

    I’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.

  • Elliot  On Wednesday, 25 March 2015 at 14:11

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

  • Oliver  On Tuesday, 7 April 2015 at 19:21

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

    • growescience  On Tuesday, 7 April 2015 at 19:28

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

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